Method and apparatus for inspection and metrology

ABSTRACT

A method including evaluating, with respect to a parameter representing remaining uncertainty of a mathematical model fitting measured data, one or more mathematical models for fitting measured data and one or more measurement sampling schemes for measuring data, against measurement data across a substrate, and identifying one or more mathematical models and/or one or more measurement sampling schemes, for which the parameter crosses a threshold.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority of U.S. application 62/146,123 whichwas filed on Apr. 10, 2015 and which is incorporated herein in itsentirety by reference.

FIELD

The present description relates to a method and apparatus for correctionof error in measured radiation distribution captured from a metrologytarget.

BACKGROUND

A lithographic apparatus is a machine that applies a desired patternonto a substrate, usually onto a target portion of the substrate. Alithographic apparatus can be used, for example, in the manufacture ofintegrated circuits (ICs) or other devices. In that instance, apatterning device, which is alternatively referred to as a mask or areticle, may be used to generate a circuit pattern to be formed on anindividual layer of the IC. This pattern can be transferred onto atarget portion (e.g., including part of, one, or several dies) on asubstrate (e.g., a silicon wafer). Transfer of the pattern is typicallyvia imaging onto a layer of radiation-sensitive material (resist)provided on the substrate. In general, a single substrate will contain anetwork of adjacent target portions that are successively patterned.Known lithographic apparatus include so-called steppers, in which eachtarget portion is irradiated by exposing an entire pattern onto thetarget portion at one time, and so-called scanners, in which each targetportion is irradiated by scanning the pattern through a radiation beamin a given direction (the “scanning”-direction) while synchronouslyscanning the substrate parallel or anti parallel to this direction. Itis also possible to transfer the pattern from the patterning device tothe substrate by imprinting the pattern onto the substrate.

SUMMARY

Manufacturing devices, such as semiconductor devices, typically involvesprocessing a substrate (e.g., a semiconductor wafer) using a number offabrication processes to form various features and multiple layers ofthe devices. Such layers and features are typically manufactured andprocessed using, e.g., deposition, lithography (which typically involvestransferring a pattern to a radiation-sensitive resist arranged on thesubstrate), etch, chemical-mechanical polishing, and ion implantation.Multiple devices may be fabricated on a plurality of dies on a substrateand then separated into individual devices.

Metrology processes are used at various steps during a devicemanufacturing process to monitor and control the process. For example,metrology processes are used to measure one or more characteristics of asubstrate, such as a relative location (e.g., overlay, alignment, etc.)or dimension (e.g., line width, critical dimension, thickness, etc.) offeatures formed on the substrate during a process, such that theperformance of the process can be determined from the one or morecharacteristics. If the one or more characteristics are unacceptable(e.g., out of a predetermined range for the characteristic(s)), themeasurements of the one or more characteristics may be used to alter oneor more parameters of the process such that further substratesmanufactured by the process have an acceptable characteristic(s).

So, significant aspects to enabling a device manufacturing processinclude developing the process itself, setting it up for monitoring andcontrol and then actually monitoring and controlling the process itself.Assuming a configuration of the fundamentals of the device manufacturingprocess (such as the patterning device pattern(s), the resist type(s),the post-lithography process steps (such as the development, etch,etc.), etc.), it is desirable to setup the lithographic apparatus fortransferring the pattern onto the substrates, develop the metrologytargets to monitor the process, setup up the metrology processes tomeasure the metrology targets and then implement a process of monitoringand controlling the process based on measurements

In an aspect, there is provided a method comprising: performing asimulation to evaluate a plurality of metrology targets and/or aplurality of metrology recipes used to measure a metrology target;identifying one or more metrology targets and/or metrology recipes fromthe evaluated plurality of metrology targets and/or metrology recipes;receiving measurement data of the one or more identified metrologytargets and/or metrology recipes; and using the measurement data to tunea metrology target parameter or metrology recipe parameter, of thesimulation.

In an aspect, there is provided a method comprising: receivingmeasurement data of a plurality of different metrology targets, eachmeasured at a plurality of metrology recipes; and using the measurementdata to verify one or more parameters of a simulation used to evaluate aplurality of metrology targets and/or a plurality of metrology recipesused to measure a metrology target.

In an aspect, there is provided a method comprising: simulating aplurality of metrology targets and/or a plurality of metrology recipestaking an expected process condition into account; identifying one ormore metrology targets and/or recipes from the simulated plurality ofmetrology targets and/or recipes; receiving measurement data of the oneor more identified metrology targets and/or recipes; and using themeasurement data to verify the expected process condition.

In an aspect, there is provided a method comprising: performing asimulation to evaluate a plurality of metrology targets and/or aplurality of metrology recipes used to measure a metrology target anddetermining a parameter representing performance of one or more of themetrology targets and/or metrology recipes; identifying one or moremetrology targets and/or metrology recipes from the evaluated pluralityof metrology targets and/or metrology recipes; receiving measurementdata of the one or more identified metrology targets and/or metrologyrecipes; and selecting, based on the measurement data and the parameter,one or more metrology targets and/or metrology recipes from theidentified one or more metrology targets and/or metrology recipes.

In an aspect, there is provided a method comprising: performing asimulation to evaluate a plurality of metrology targets and a pluralityof metrology recipes used to measure a metrology target; identifying oneor more combinations of metrology target and metrology recipe from theevaluated plurality of metrology targets and metrology recipes;formulating a plurality of metrology recipes for the one or moremetrology targets from the identified one or more combinations based onthe one or more metrology recipes from the identified one or morecombinations; and receiving measurement data of the one or moremetrology targets from the identified one or more combinations measuredusing the formulated plurality of metrology recipes.

In an aspect, there is provided a method comprising: determining aparameter representative of sensitivity of one or more metrologyrecipes, or one or more metrology recipe parameters, to one or moremetrology targets based on measurement data of a metrology targetmeasured at a plurality of metrology recipes; and evaluating, based onthe parameter representative of sensitivity, a plurality of metrologyrecipes used to measure the metrology target by simulation or againstmeasured data to identify one or more metrology recipes of the pluralityof metrology recipes for use in measuring the metrology target.

In an aspect, there is provided a method comprising: evaluating aplurality of metrology targets and/or a plurality of metrology recipesused to measure a metrology target by simulation or against measureddata; and identifying one or more metrology targets and/or metrologyrecipes from the evaluated plurality of metrology targets and/ormetrology recipes for which diffraction efficiency, or a parameterderived from diffraction efficiency, crosses a threshold.

In an aspect, there is provided a method comprising: evaluating aplurality of metrology targets and/or a plurality of metrology recipesused to measure a metrology target by simulation or against measureddata; and identifying one or more metrology targets and/or metrologyrecipes from the evaluated plurality of metrology targets and/ormetrology recipes for which a measurement apparatus property, or aparameter derived from the measurement apparatus property, crosses athreshold.

In an aspect, there is provided a method comprising: evaluating, withrespect to a parameter representing remaining uncertainty of amathematical model fitting measured data, one or more mathematicalmodels for fitting measured data and one or more measurement samplingschemes for measuring data, against measurement data across a substrate;and identifying one or more mathematical models and/or one or moremeasurement sampling schemes for which the parameter crosses athreshold.

In an aspect, there is provided a method comprising: evaluating, withrespect to a first evaluation parameter and a second differentevaluation parameter, one or more mathematical models for fittingmeasured data and one or more measurement sampling schemes for measuringdata, against measurement data across a substrate; and identifying oneor more mathematical models and/or one or more measurement samplingschemes for which the first and second evaluation parameters cross athreshold.

In an aspect, there is provided a method of determining a samplingscheme for measuring data and/or a mathematical model for fittingmeasured data, to monitor a process step in a lithographic process, themethod comprising: determining the sampling scheme and the mathematicalmodel at least partially based on a through-put model of an inspectionapparatus.

In an aspect, there is provided a method comprising: receivingmeasurement data of a metrology target measured according to a metrologyrecipe; determining a sampling scheme for measuring data with themetrology target using the metrology recipe at least partially based ona through-put model of an inspection apparatus; determining anevaluation parameter based on the measurement data and the samplingscheme; determining if the evaluation parameter crosses a threshold; andchanging the sampling scheme at least partially based on the through-putmodel if the evaluation parameter is determined to cross the threshold.

In an aspect, there is provided a method comprising: displaying aplurality of graphical user interface elements, each graphical userinterface element representing a step in a measurement design, setupand/or monitoring process and each graphical user interface elementenabling access by the user to further steps in the measurement design,setup and/or monitoring process for the associated step of the graphicaluser interface element; and displaying an indicator associated with oneor more of the plurality of graphical user elements, the indicatorindicating that a step in the measurement design, setup and/ormonitoring process is not completed and/or that a key performanceindicator associated with a step in the measurement design, setup and/ormonitoring process has passed a threshold.

In an aspect, there is provided a non-transitory computer programproduct comprising machine-readable instructions for causing a processorto cause performance of a method as described herein.

In an aspect, there is provided a system comprising: an inspectionapparatus configured to provide a beam on a measurement target on asubstrate and to detect radiation redirected by the target to determinea parameter of a lithographic process; and the non-transitory computerprogram product as described herein. In an embodiment, the systemfurther comprises a lithographic apparatus comprising a supportstructure configured to hold a patterning device to modulate a radiationbeam and a projection optical system arranged to project the modulatedonto a radiation-sensitive substrate.

In an aspect, there is provided a system comprising: an alignmentsensor, comprising: an output to provide radiation from a radiationsource onto a target, a detector configured to receive radiation fromthe target, and a control system configured to determine alignment oftwo or more objects responsive to the received radiation; and thenon-transitory computer program product as described herein. In anembodiment, the system further comprises a lithographic apparatuscomprising a support structure configured to hold a patterning device tomodulate a radiation beam and a projection optical system arranged toproject the modulated onto a radiation-sensitive substrate.

In an aspect, there is provided a system comprising: a level sensor,comprising: an output to provide radiation from a radiation source ontoa surface, a detector configured to receive radiation from the surface,and a control system configured to determine a position of the surfaceresponsive to the received radiation; and the non-transitory computerprogram product as described herein. In an embodiment, the systemfurther comprises a lithographic apparatus comprising a supportstructure configured to hold a patterning device to modulate a radiationbeam and a projection optical system arranged to project the modulatedonto a radiation-sensitive substrate.

In an aspect, there is provided a method of manufacturing deviceswherein a device pattern is applied to a series of substrates using alithographic process, the method comprising: inspecting a target asidentified using a method as described herein and/or inspecting a targetusing a metrology recipe as identified using a method as describedherein, the target formed as part of or beside the device pattern on atleast one of the substrates; and controlling the lithographic processfor later substrates in accordance with the result of the inspecting.

In an aspect, there is provided a method of manufacturing deviceswherein a device pattern is applied to a series of substrates using alithographic process, the method including inspecting at least a targetformed as part of or beside the device pattern on at least one of thesubstrates using a sampling scheme as determined using a method asdescribed herein, and controlling the lithographic process for the atleast one substrate or another substrate in accordance with the resultof the inspecting.

In an aspect, there is provided a method of manufacturing deviceswherein a device pattern is applied to a series of substrates using alithographic process, the method including inspecting at least a targetformed as part of or beside the device pattern on at least one of thesubstrates, wherein the inspecting is performed using a sampling schemeas identified using a method as described herein and/or the measureddata from the inspecting is modeled using a mathematical model asidentified using a method as described herein, and controlling thelithographic process for the at least one substrate or another substratein accordance with the result of the inspecting.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will now be described, by way of example only, withreference to the accompanying drawings in which:

FIG. 1 schematically depicts an embodiment of a lithographic apparatus;

FIG. 2 schematically depicts an embodiment of a lithographic cell orcluster;

FIG. 3 schematically depicts a flow diagram of an embodiment of part ofdevice manufacturing process development, monitoring and control;

FIG. 4 schematically depicts a flow diagram of an embodiment ofmetrology setup;

FIG. 5 schematically depicts a flow diagram of an embodiment ofmetrology target design;

FIG. 6 schematically depicts a flow diagram of an embodiment ofmetrology target design selection and qualification;

FIG. 7 schematically depicts a flow diagram of an embodiment of furthermetrology target design qualification;

FIG. 8 schematically depicts a flow diagram of an embodiment ofmetrology target design, selection and qualification;

FIG. 9 schematically depicts a flow diagram of an embodiment ofmeasurement data mathematical model and sampling scheme evaluation;

FIG. 10 schematically depicts a flow diagram of an embodiment of amethod of verifying expected performance; and

FIG. 11 schematically depicts a user interface of software to providefor an embodiment of part of device manufacturing process development,monitoring and control.

DETAILED DESCRIPTION

Before describing embodiments in detail, it is instructive to present anexample environment in which embodiments may be implemented.

FIG. 1 schematically depicts a lithographic apparatus LA. The apparatuscomprises:

-   -   an illumination system (illuminator) IL configured to condition        a radiation beam B (e.g. UV radiation or DUV radiation);    -   a support structure (e.g. a mask table) MT constructed to        support a patterning device (e.g. a mask) MA and connected to a        first positioner PM configured to accurately position the        patterning device in accordance with certain parameters;    -   a substrate table (e.g. a wafer table) WT constructed to hold a        substrate (e.g. a resist-coated wafer) W and connected to a        second positioner PW configured to accurately position the        substrate in accordance with certain parameters; and    -   a projection system (e.g. a refractive projection lens system)        PL configured to project a pattern imparted to the radiation        beam B by patterning device MA onto a target portion C (e.g.        comprising one or more dies) of the substrate W, the projection        system supported on a reference frame (RF).

The illumination system may include various types of optical components,such as refractive, reflective, magnetic, electromagnetic, electrostaticor other types of optical components, or any combination thereof, fordirecting, shaping, or controlling radiation.

The support structure supports the patterning device in a manner thatdepends on the orientation of the patterning device, the design of thelithographic apparatus, and other conditions, such as for examplewhether or not the patterning device is held in a vacuum environment.The support structure can use mechanical, vacuum, electrostatic or otherclamping techniques to hold the patterning device. The support structuremay be a frame or a table, for example, which may be fixed or movable asrequired. The support structure may ensure that the patterning device isat a desired position, for example with respect to the projectionsystem. Any use of the terms “reticle” or “mask” herein may beconsidered synonymous with the more general term “patterning device.”

The term “patterning device” used herein should be broadly interpretedas referring to any device that can be used to impart a radiation beamwith a pattern in its cross-section such as to create a pattern in atarget portion of the substrate. It should be noted that the patternimparted to the radiation beam may not exactly correspond to the desiredpattern in the target portion of the substrate, for example if thepattern includes phase-shifting features or so called assist features.Generally, the pattern imparted to the radiation beam will correspond toa particular functional layer in a device being created in the targetportion, such as an integrated circuit.

The patterning device may be transmissive or reflective. Examples ofpatterning devices include masks, programmable mirror arrays, andprogrammable LCD panels. Masks are well known in lithography, andinclude mask types such as binary, alternating phase-shift, andattenuated phase-shift, as well as various hybrid mask types. An exampleof a programmable mirror array employs a matrix arrangement of smallmirrors, each of which can be individually tilted so as to reflect anincoming radiation beam in different directions. The tilted mirrorsimpart a pattern in a radiation beam, which is reflected by the mirrormatrix.

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors such as the use ofan immersion liquid or the use of a vacuum. Any use of the term“projection lens” herein may be considered as synonymous with the moregeneral term “projection system”.

As here depicted, the apparatus is of a transmissive type (e.g.employing a transmissive mask). Alternatively, the apparatus may be of areflective type (e.g. employing a programmable mirror array of a type asreferred to above, or employing a reflective mask).

The lithographic apparatus may be of a type having two (dual stage) ormore tables (e.g., two or more substrate tables WTa, WTb, two or morepatterning device tables, a substrate table WTa and a table WTb belowthe projection system without a substrate that is dedicated to, forexample, facilitating measurement, and/or cleaning, etc.). In such“multiple stage” machines the additional tables may be used in parallel,or preparatory steps may be carried out on one or more tables while oneor more other tables are being used for exposure. For example, alignmentmeasurements using an alignment sensor AS and/or level (height, tilt,etc.) measurements using a level sensor LS may be made.

The lithographic apparatus may also be of a type wherein at least aportion of the substrate may be covered by a liquid having a relativelyhigh refractive index, e.g. water, so as to fill a space between theprojection system and the substrate. An immersion liquid may also beapplied to other spaces in the lithographic apparatus, for example,between the patterning device and the projection system. Immersiontechniques are well known in the art for increasing the numericalaperture of projection systems. The term “immersion” as used herein doesnot mean that a structure, such as a substrate, must be submerged inliquid, but rather only means that liquid is located between theprojection system and the substrate during exposure.

Referring to FIG. 1, the illuminator IL receives a radiation beam from aradiation source SO. The source and the lithographic apparatus may beseparate entities, for example when the source is an excimer laser. Insuch cases, the source is not considered to form part of thelithographic apparatus and the radiation beam is passed from the sourceSO to the illuminator IL with the aid of a beam delivery system BDcomprising, for example, suitable directing mirrors and/or a beamexpander. In other cases the source may be an integral part of thelithographic apparatus, for example when the source is a mercury lamp.The source SO and the illuminator IL, together with the beam deliverysystem BD if required, may be referred to as a radiation system.

The illuminator IL may comprise an adjuster AD configured to adjust theangular intensity distribution of the radiation beam. Generally, atleast the outer and/or inner radial extent (commonly referred to as6-outer and 6-inner, respectively) of the intensity distribution in apupil plane of the illuminator can be adjusted. In addition, theilluminator IL may comprise various other components, such as anintegrator IN and a condenser CO. The illuminator may be used tocondition the radiation beam, to have a desired uniformity and intensitydistribution in its cross-section.

The radiation beam B is incident on the patterning device (e.g., mask)MA, which is held on the support structure (e.g., mask table) MT, and ispatterned by the patterning device. Having traversed the patterningdevice MA, the radiation beam B passes through the projection system PL,which focuses the beam onto a target portion C of the substrate W. Withthe aid of the second positioner PW and position sensor IF (e.g. aninterferometric device, linear encoder, 2-D encoder or capacitivesensor), the substrate table WT can be moved accurately, e.g. so as toposition different target portions C in the path of the radiation beamB. Similarly, the first positioner PM and another position sensor (whichis not explicitly depicted in FIG. 1) can be used to accurately positionthe patterning device MA with respect to the path of the radiation beamB, e.g. after mechanical retrieval from a mask library, or during ascan. In general, movement of the support structure MT may be realizedwith the aid of a long-stroke module (coarse positioning) and ashort-stroke module (fine positioning), which form part of the firstpositioner PM. Similarly, movement of the substrate table WT may berealized using a long-stroke module and a short-stroke module, whichform part of the second positioner PW. In the case of a stepper (asopposed to a scanner) the support structure MT may be connected to ashort-stroke actuator only, or may be fixed. Patterning device MA andsubstrate W may be aligned using patterning device alignment marks M1,M2 and substrate alignment marks P1, P2. Although the substratealignment marks as illustrated occupy dedicated target portions, theymay be located in spaces between target portions (these are known asscribe-lane alignment marks). Similarly, in situations in which morethan one die is provided on the patterning device MA, the patterningdevice alignment marks may be located between the dies.

The depicted apparatus could be used in at least one of the followingmodes:

1. In step mode, the support structure MT and the substrate table WT arekept essentially stationary, while an entire pattern imparted to theradiation beam is projected onto a target portion C at one time (i.e. asingle static exposure). The substrate table WT is then shifted in the Xand/or Y direction so that a different target portion C can be exposed.In step mode, the maximum size of the exposure field limits the size ofthe target portion C imaged in a single static exposure.

2. In scan mode, the support structure MT and the substrate table WT arescanned synchronously while a pattern imparted to the radiation beam isprojected onto a target portion C (i.e. a single dynamic exposure). Thevelocity and direction of the substrate table WT relative to the supportstructure MT may be determined by the (de-)magnification and imagereversal characteristics of the projection system PL. In scan mode, themaximum size of the exposure field limits the width (in the non-scanningdirection) of the target portion in a single dynamic exposure, whereasthe length of the scanning motion determines the height (in the scanningdirection) of the target portion.

3. In another mode, the support structure MT is kept essentiallystationary holding a programmable patterning device, and the substratetable WT is moved or scanned while a pattern imparted to the radiationbeam is projected onto a target portion C. In this mode, generally apulsed radiation source is employed and the programmable patterningdevice is updated as required after each movement of the substrate tableWT or in between successive radiation pulses during a scan. This mode ofoperation can be readily applied to maskless lithography that utilizesprogrammable patterning device, such as a programmable mirror array of atype as referred to above.

Combinations and/or variations on the above described modes of use orentirely different modes of use may also be employed.

As shown in FIG. 2, the lithographic apparatus LA may form part of alithographic cell LC, also sometimes referred to a lithocell or cluster,which also includes apparatuses to perform pre- and post-exposureprocesses on a substrate. Conventionally these include one or more spincoaters SC to deposit one or more resist layers, one or more developersDE to develop exposed resist, one or more chill plates CH and/or one ormore bake plates BK. A substrate handler, or robot, RO picks up one ormore substrates from input/output port 1/O1, 1/O2, moves them betweenthe different process apparatuses and delivers them to the loading bayLB of the lithographic apparatus. These apparatuses, which are oftencollectively referred to as the track, are under the control of a trackcontrol unit TCU which is itself controlled by the supervisory controlsystem SCS, which also controls the lithographic apparatus vialithography control unit LACU. Thus, the different apparatuses can beoperated to maximize throughput and processing efficiency.

In order that a substrate that is exposed by the lithographic apparatusis exposed correctly and consistently, it is desirable to inspect anexposed substrate to measure one or more properties such as overlayerror between subsequent layers, line thickness, critical dimension(CD), focus offset, a material property, etc. Accordingly amanufacturing facility in which lithocell LC is located also typicallyincludes a metrology system MET which receives some or all of thesubstrates W that have been processed in the lithocell. The metrologysystem MET may be part of the lithocell LC, for example it may be partof the lithographic apparatus LA.

Metrology results may be provided directly or indirectly to thesupervisory control system SCS. If an error is detected, an adjustmentmay be made to exposure of a subsequent substrate (especially if theinspection can be done soon and fast enough that one or more othersubstrates of the batch are still to be exposed) and/or to subsequentexposure of the exposed substrate. Also, an already exposed substratemay be stripped and reworked to improve yield, or discarded, therebyavoiding performing further processing on a substrate known to befaulty. In a case where only some target portions of a substrate arefaulty, further exposures may be performed only on those target portionswhich are good.

Within a metrology system MET, an inspection apparatus is used todetermine one or more properties of the substrate, and in particular,how one or more properties of different substrates vary or differentlayers of the same substrate vary from layer to layer. The inspectionapparatus may be integrated into the lithographic apparatus LA or thelithocell LC or may be a stand-alone device. To enable rapidmeasurement, it is desirable that the inspection apparatus measure oneor more properties in the exposed resist layer immediately after theexposure. However, the latent image in the resist has a lowcontrast—there is only a very small difference in refractive indexbetween the parts of the resist which have been exposed to radiation andthose which have not—and not all inspection apparatus have sufficientsensitivity to make useful measurements of the latent image. Thereforemeasurements may be taken after the post-exposure bake step (PEB) whichis customarily the first step carried out on an exposed substrate andincreases the contrast between exposed and unexposed parts of theresist. At this stage, the image in the resist may be referred to assemi-latent. It is also possible to make measurements of the developedresist image—at which point either the exposed or unexposed parts of theresist have been removed—or after a pattern transfer step such asetching. The latter possibility limits the possibilities for rework of afaulty substrate but may still provide useful information.

In order to monitor the device manufacturing process that includes atleast one lithography step, the patterned substrate is inspected and oneor more parameters of the patterned substrate are measured. The one ormore parameters may include, for example, the overlay error betweensuccessive layers formed in or on the patterned substrate, criticallinewidth (e.g., critical dimension (CD)) of developed photosensitiveresist, focus or focus error of the lithography, dose or dose error ofthe lithography, aberrations of the lithography, etc. This measurementmay be performed on a target of the product substrate itself and/or on adedicated metrology target provided on the substrate. There are varioustechniques for making measurements of the structures formed in thedevice manufacturing process, including the use of a scanning electronmicroscope, image-based measurement or inspection tools and/or variousspecialized tools. A fast and non-invasive form of specialized metrologyand/or inspection tool is one in which a beam of radiation is directedonto a target on the surface of the substrate and properties of thescattered (diffracted/reflected) beam are measured. By comparing one ormore properties of the beam before and after it has been scattered bythe substrate, one or more properties of the substrate can bedetermined. This may be termed diffraction-based metrology orinspection. A particular application of this diffraction-based metrologyor inspection is in the measurement of feature asymmetry within aperiodic target. This can be used as a measure of overlay error, forexample, but other applications are also known. For example, asymmetrycan be measured by comparing opposite parts of the diffraction spectrum(for example, comparing the −1st and +1^(st) orders in the diffractionspectrum of a periodic grating). This can be done simply as isdescribed, for example, in U.S. patent application publicationUS2006-066855, which is incorporated herein in its entirety byreference.

Significant aspects to enabling a device manufacturing process includedeveloping the process itself, setting it up for monitoring and controland then actually monitoring and controlling the process itself.Assuming a configuration of the fundamentals of the device manufacturingprocess (such as the patterning device pattern(s), the resist type(s),the post-lithography process steps (such as the development, etch,etc.), etc.), it is desirable to setup the lithographic apparatus fortransferring the pattern onto the substrates, develop the metrologytargets to monitor the process, setup up the metrology processes tomeasure the metrology targets and then implement a process of monitoringand controlling the process based on measurements. While discussion inthis application will consider an embodiment of a metrology targetdesigned to measure overlay between one or more layers of a device beingformed on a substrate, the embodiments herein are equally applicable toother metrology targets, such as targets to measure alignment (e.g.,between a patterning device and a substrate), targets to measurecritical dimension, etc. Accordingly, the references herein to overlaymetrology targets, overlay data, etc. should be considered as suitablymodified to enable other kinds of targets and metrology processes.

Referring to FIG. 3, a high level overview of a development, monitoringand control process is shown. These various steps shown in FIG. 3 areeach implemented at least in part with software. In an embodiment, thesoftware associated with each of the steps is integrated together sothat results, designs, data, etc. as applicable from one of the portionsof the integrated software application may be shared as, e.g., an inputto another one of the portions of the integrated software application.

As noted above, at 300, the lithographic apparatus may be setup forexecuting the lithography aspect of the device manufacturing process andoptionally, may be configured to correct for deviations occurring withinthe lithographic apparatus or in other processes in the devicemanufacturing process. Such setup includes setting one or moreparameters of the lithographic apparatus.

In an embodiment, the setup may include establishing a baseline setup ofa lithographic apparatus and enabling the subsequent monitoring of thelithographic apparatus and adjustment of one or more parameters of thelithographic apparatus. For example, a lithographic apparatus can be setup for optimal operation as its baseline setup. Such a setup may bematched to other lithographic apparatuses in the factory. But, overtime, system performance parameters will drift. Besides stoppingproduction and recalibrating or rematching, one or more monitorsubstrates may be exposed and measured, e.g., using metrology systemMET, to capture one or more performance parameters of the lithographicapparatus, such as the lithographic apparatus' overlay grid and focuscalibration state per substrate table. Based on these measurements, oneor more parameters are identified whose correction or change would beable to return the lithographic apparatus to its baseline setup.Further, updated values of the identified one or more parameters arecalculated to return the lithographic apparatus to optimal operation.Then while production continues, the one or more lithographic apparatusparameters are automatically updated based on the measured parameters toreturn the lithographic apparatus to its baseline. Such a “reset” mayoccur, for example, once a day or other recurring time period.Optionally, the software can decide when the updates should be appliedand whether they need to be overwritten on the lithographic apparatus orswitched off for a certain time. An example of such software is ASML'sBaseliner software.

In an embodiment, one or more inspection apparatus may be setup forexecuting the lithography aspect of the device manufacturing process andoptionally, may be configured to correct for deviations occurring withinthe inspection apparatus or in other processes in the devicemanufacturing process. Such setup includes setting one or moreparameters of the inspection apparatus. Such an inspection apparatus maya diffraction-based overlay metrology tool that can measure, e.g.,overlay, critical dimension and/or other parameters. Such an inspectionapparatus may be an alignment apparatus used to measure relativeposition between two objects, such as between a patterning device and asubstrate. Such an inspection apparatus may be a level sensor to measurea position of a surface, e.g., a height and/or rotational position of asubstrate surface.

In an embodiment, the setup may include establishing a baseline setup ofan inspection apparatus and enabling the subsequent monitoring of theinspection apparatus and adjustment of one or more parameters of theinspection apparatus. For example, an inspection apparatus can be set upfor optimal operation as its baseline setup. Such a setup may be matchedto other inspection apparatuses in the factory. But, over time, systemperformance parameters will drift. Besides stopping production andrecalibrating or rematching, one or more monitor substrates may beexposed and measured, e.g., using the inspection apparatus or metrologysystem MET, to capture one or more performance parameters of theinspection apparatus. Based on these measurements, one or moreparameters are identified whose correction or change would be able toreturn the inspection apparatus to its baseline setup. Further, updatedvalues of the identified one or more parameters are calculated to returnthe inspection apparatus to optimal operation. Then while productioncontinues, the one or more inspection apparatus parameters areautomatically updated based on the measured parameters to return theinspection apparatus to its baseline. Such a “reset” may occur, forexample, once a day or other recurring time period. Optionally, thesoftware can decide when the updates should be applied and whether theyneed to be overwritten on the inspection apparatus or switched off for acertain time.

At 310, metrology may be setup for the device manufacturing process. Inan embodiment, this setup includes design of one or more metrologytargets for the device manufacturing process. For example, one or moreoverlay metrology targets for exposing on a substrate during productionmay be developed. Further, a metrology recipe for the one or moremetrology targets may be developed. A metrology recipe is one or moreparameters (and one or more associated values) associated with themetrology apparatus itself used to measure the one or more metrologytargets and/or the measurement process, such as one or more wavelengthsof the measurement beam, one or more types of polarization of themeasurement beam, one or more dose values of the measurement beam, oneor more bandwidths of the measurement beam, one or more aperturesettings of the inspection apparatus used with the measurement beam, thealignment marks used to locate the measurement beam on the target, thealignment scheme used, the sampling scheme, the layout of the metrologytargets and the movement scheme to measure the targets and/or points ofinterest of a target, etc. In an embodiment, the one or more metrologytargets may be qualified for the device manufacturing process. Forexample, a plurality of metrology target designs may be evaluated toidentify the one or more metrology targets that minimize residualvariation (systematic and/or random). In an embodiment, a plurality ofmetrology target designs may be evaluated to identify the one or moremetrology targets whose performance match the device, e.g., identify ametrology target whose measure of overlay error matches the overlayerror of the device. The metrology target may be design, e.g., formeasurement of overlay, of focus, of critical dimension (CD), ofalignment, of asymmetry in the target, etc. and any combination thereof.

Further, a device manufacturing process may have a particular systematicvariation (fingerprint) arising from the nature of the process. Forexample, the device manufacturing process may call for use of particularsubstrate tables in the lithocell LC, use of specific etching ordevelopment types, use of particular baking parameters, use ofparticular focus and dose settings, etc. which may result in aparticular regular variation in the exposure of a plurality ofsubstrates. So, at 320, the process may be setup by determining acorrection to be applied to one or more parameters of the devicemanufacturing process (e.g., one or more parameters of the lithographicapparatus, one or more parameters of the track, etc.) to account for asystematic variation arising from the particular device manufacturingprocess. This may result in a high order set of corrections to thebaseline setup as described above. To arrive at the correction, theprocess fingerprint may be estimated by simulation and/or bymeasurements of substrates exposed in a development phase. From theprocess fingerprint, one or more lithographic and/or process correctionmodels may be developed that can be applied to modify the lithographicapparatus, the track, etc. to at least partially correct the processfingerprint.

The lithographic apparatus setup 300, metrology setup 310 and processsetup 320 may be together considered part of a process development phase330. In addition to process development, steps should be taken tomonitor and control the device manufacturing process during high volumemanufacturing (HVM).

At 340, the metrology process is configured to enable measuring of theone or more metrology targets to enable monitoring and control of thedevice manufacturing process at 350. It may be too time consuming tomeasure every metrology target for every substrate of every lot (a lotis a batch of substrates of typically identical characteristics that areprocessed together during a run of the device manufacturing process; alot of substrates is typically kept together in a movable container suchas a FOUP). So, a measurement sampling scheme may be established formeasuring the one or more metrology targets. A sampling scheme for ametrology process may include one or more parameters selected from:number of substrates per lot sampled; numeric designation of thesubstrate(s) in a lot or per lot sampled; number of fields sampled;locations of sampled fields on the substrate; number of sites in eachfield; locations of the sites in the field; frequency of samples; typeof metrology target; or measurement algorithm. In an embodiment, thesampling scheme is designed to minimize variation. For example, thesampling scheme may be selected to minimize substrate to substratevariation, lot to lot variation, and/or machine to machine variation(e.g., variation between lithographic apparatuses in a factory).Further, one or more key performance indicators (KPIs) may be identifiedand one or more thresholds associated with the KPIs may be determined toenable process control. For example, mean, variation, etc. may beidentified as KPIs and thresholds (e.g., value not to exceed, value notto go below, etc.) may be determined to use as control limits of theprocess. Further, it is possible to model the measurement results of themetrology targets using one or more measurement data mathematical modelsthat are appropriately parameterized (i.e., a mathematical model withappropriately decided and defined parameters, and values thereof asapplicable, to fit (where fit means not necessarily a perfect fit withall data) data to the mathematical model). So, a measurement datamathematical model may be established for measuring the one or moremetrology targets. In an embodiment, the measurement data mathematicalmodel and sampling scheme are established together. In an embodiment,the mathematical model may comprise one or more basis functionsspecified by one or more parameters; typically, the mathematical modelmay comprise a combination of a plurality of basis functions. In anembodiment, the mathematical model is parameterized with values for theparameters to fit the data.

Referring to FIG. 4, a more detailed flow diagram of an embodiment ofmetrology setup is depicted. At 400, data for the design of one or moremetrology targets is obtained or provided. For example, the data mayinclude, for example, information regarding the nature of one or morelayers produced using the device manufacturing process (and to which theone or more metrology targets would be applied). This may be referred toas stack information. Such data may include information regardingparameters such as layer thickness, layer material, layer refractiveindex, layer absorption index, etc. and may include variation dataassociated with such parameters (e.g., a range of expected variationassociated with the parameters). The data may include, for example,information regarding the nature of the one or more processes associatedwith the one or more layers. Such data may include the type and/orparameters of etch, the type and/or parameters of post-exposure baking,the type and/or parameters of development of resist, etc. and mayinclude variation data associated with such parameters (e.g., a range ofexpected variation associated with the parameters). The data mayinclude, for example, an overlay tree, which specifies between whichlayers of a plurality of layers overlay measurement is desired.

At 405, one or more metrology target designs are determined. In anembodiment, the one or more metrology targets design are determined by asimulation program that simulates the device manufacturing process andthe measurement process of candidate target designs based on, e.g., theapplicable full layer stack, to allow design parameters of the targetfor a given layer to be optimized. Thus, in the simulation, one or moredesign parameters of the target may be fixed or allowed to vary. Suchparameters may include the pitch of a periodic structure of the target,a critical dimension of features of a periodic structure of the target,a thickness, etc. Further, one or more parameters of the metrologyrecipe (e.g., measurement beam wavelength, measurement beampolarization, measurement beam dose, aperture setting associated withthe measurement beam, etc.) may be fixed or allowed to vary. In anembodiment, the software accepts, or provides a user interface to allowdefinition of, specification of the stack and process (e.g., layermaterial, etch type, deposition type, polishing (e.g., CMP) process,etc.), indications of which one or more parameters may be fixed andwhich may vary, specification of the range of variability of varyingparameters, design rules or constraints, etc.

Once the starting conditions are specified, the software can run asimulation to identify one or more metrology target designs, one or moremetrology recipes (e.g., for a particular metrology target design)and/or one or more combinations of metrology design and metrology recipethat meet printability, detectability, throughput, process stability(e.g., sensitivity to process variation), and/or tool dependency (e.g.,a sensitivity to an inspection apparatus-specific parameter)specifications. The overlay accuracy and lens aberration performance canbe further determined through simulation.

So, for example, based on the conditions of the stack and the devicemanufacturing process, a simulation model (such as an image/resist modeland resist processing model that optionally may be particularlyconfigured for the capabilities of a particular lithographic or otherapparatus) may be used to determine how various metrology target designswith different design parameters and/or how various metrology targetrecipes with different recipe parameters, would be produced for theapplicable device manufacturing process. For example, by includinginformation regarding the exposure process, the sensitivity of metrologytarget design to projection system aberration can be matched to that ofcritical device features being printed in the specified layer, enablingoverlay gains. Further, a simulation model of the measurement process(e.g., a diffraction simulation model that optionally may beparticularly configured for the measurement capabilities of a particularinspection apparatus) may be used to evaluate the various metrologytarget designs against a specified or varying metrology recipe (e.g.,different wavelengths, different polarizations, different doses, etc.)and/or evaluate a metrology target design for varying metrology recipes.The result may be a ranking by, or measure of, performance (e.g.,printability, detectability, throughput, process stability, tooldependency, etc.) of various metrology target designs and/or metrologyrecipes to allow selection by a user, or by automatic process, of one ormore metrology target designs and/or one or more metrology recipes.Where one or more parameters of the metrology recipe are allowed tovary, the results for a metrology target design may include anassociated specification of the one or more parameters of the metrologyrecipe for the various metrology target designs. So, for example, aranking may be presented of the metrology target designs, may bepresented of the metrology target designs, may be presented ofcombinations of metrology target design and metrology recipe (such that,for example, a particular metrology target design may have multiplemetrology recipes yielding multiple combinations of a same metrologytarget design with different metrology recipes, etc.) where the baseranking may be on the metrology target design or on the metrologyrecipe, etc.

Further, in an embodiment, the robustness of the various metrologytarget designs and/or metrology recipes to process variation may beevaluated by allowing a perturbation of one of more parameters (e.g.,according to variation data) to determine sensitivity of the variousmetrology target designs and/or metrology recipes to various parameterperturbations. The perturbation may be to an etch parameter, to apolishing process parameter, to critical dimension of a structure of thetarget, etc. The result may be a ranking by, or measure of, robustnessof various metrology target designs and/or metrology recipes to allowselection by a user, or by automatic process, of one or more metrologytarget designs and/or metrology recipes. One or more of the identifiedmetrology target designs and/or metrology recipes may be selected foruse or further evaluation and where a metrology target design isinvolved, the software may output a patterning device pattern for theone or more identified metrology target design in, e.g., GDS format.Thus, the software can evaluate thousands, if not millions, of metrologytarget designs and/or metrology recipes and thus allow the design spaceto be well explored by identifying metrology target designs and/ormetrology recipes that balance precision and accuracy.

At 410, the one or more metrology target designs and/or metrologyrecipes from 405 (typically a plurality of metrology target designsand/or metrology recipes) are further evaluated experimentally. Inparticular, a plurality of metrology recipes for an inspection apparatusmay be determined for each metrology target design (which may includethe one or more metrology recipes from 405 where one or more metrologyrecipes are output) and then the one or more metrology target designsare created and measured at each metrology recipe using the inspectionapparatus. Each metrology target design is evaluated against theplurality of metrology recipes to enable determination of a suitable oroptimal recipe. In an embodiment, a total measurement uncertainty of oneor more of the metrology target designs is determined. In an embodiment,the accuracy (e.g., by use of a residual) of one or more of themetrology target designs is determined. From the various results, aranking by, or measure of, performance of the evaluated one or moremetrology target designs and/or metrology recipes may be created toallow selection by a user, or by automatic process, of one or moremetrology target designs and/or metrology recipes from the evaluated oneor more metrology target designs and/or metrology recipes.

At 415, the one or more metrology target designs and/or metrologyrecipes from 410 (typically a plurality of metrology target designsand/or metrology recipes) are further evaluated experimentally. In anembodiment, the accuracy (e.g., by use of a residual) of one or more ofthe metrology target designs and/or metrology recipes is determined.From the various results, a ranking by, or measure of, performance ofthe evaluated one or more metrology target designs and/or metrologyrecipes may be created to allow selection by a user, or by automaticprocess, of one or more metrology target designs and/or metrologyrecipes from the evaluated one or more metrology target designs and/ormetrology recipes.

At 420, where, e.g., more than one inspection apparatus is used tomeasure the one or more metrology targets in, e.g., process developmentand/or HVM and/or a different inspection apparatus is used forevaluation than in, e.g., process development and/or HVM, the one ormore metrology target designs and/or metrology recipes from 410(typically a plurality of metrology target designs) are furtherevaluated experimentally using the plurality of inspection apparatuses.In an embodiment, a correction for one or more of the inspectionapparatuses may be determined based on the measurements of the one ormore metrology target designs and/or with the one or more metrologyrecipes. In an embodiment, the correction may be such that theinspection apparatuses having matching performance.

At 425, the one or more identified and evaluated metrology targetdesigns and/or metrology recipes are ready for use in HVM. Where thereis a plurality of metrology target designs and/or metrology recipes, auser may select which one or more metrology target designs and/ormetrology recipes are appropriate for the device manufacturing process.

At 430, feedback information may be provided for the next preparationand supply of data 400. Using the feedback information, the data 400 maybe improved or better selected.

Referring to 435, the processes 405, 410, 415 and 420 would be repeatedfor each layer/metrology step. That is, those processes are repeated foreach layer designed to have a metrology target being measured by ameasurement step and for each measurement step involving that layer(e.g., a target in a layer may be used for measuring different layers,whether at a same measurement time or at different times in the devicemanufacturing process). So, a plurality of metrology target designs areevaluated for each layer designed to have a metrology target and furtherevaluated against each measurement step associated therewith.

Referring to 440, process 410 is repeated per metrology target designand/or metrology recipe, which may be each metrology target designand/or metrology recipe from process 405. For example, it may involveevaluating about 10-40 metrology target designs. The outcome of process410 may be one or more of the starting metrology target designs and/ormetrology recipes, e.g., a subset of 2-15 metrology target designs.Referring to 445, process 415 is repeated per metrology target designand/or metrology recipe, which may be each metrology target designand/or metrology recipe from process 410. For example, it may involveevaluating about 2-15 metrology target designs. The outcome of process415 may be one or more of the starting metrology target designs and/ormetrology recipes, e.g., a subset of 1-10 metrology target designs.Referring to 450, process 420 is repeated per metrology target designand/or metrology recipe, which may be each metrology target designand/or metrology recipe from process 415. For example, it may involveevaluating about 1-10 metrology target designs. The outcome of process420 may be one or more of the starting metrology target designs and/ormetrology recipes, e.g., 1-5 metrology target designs.

Referring to FIG. 5, details of an embodiment of process 405 arepresented. As described above, using data 400, one or more metrologytargets design are determined at 500 by a simulation program thatsimulates the device manufacturing process and the measurement processof candidate target designs based on, e.g., the applicable full layerstack, to allow design parameters of the target for a given layer to beoptimized. As noted above, in the simulation, one or design parametersof the target may be fixed or allowed to vary. Such parameters mayinclude the pitch of a periodic structure of the target, a criticaldimension of a structural feature, a thickness, etc. Further, one ormore parameters of the metrology recipe (e.g., measurement beamwavelength, measurement beam polarization, measurement beam dose,aperture setting associated with the measurement beam, etc.) may befixed or allowed to vary. In an embodiment, at 505, the softwareaccepts, or provides a user interface to allow definition of,specification of the stack and process (e.g., layer material, etch type,deposition type, polishing (e.g., CMP) process, etc.), indications ofwhich one or more parameters may be fixed and which may vary,specification of the range of variability of varying parameters, designrules or constraints, etc.

At 510, a ranking by, or measure of, performance (e.g., printability,detectability, robustness, etc. or a combination thereof, including aweighted combination) of various metrology target designs are providedto allow selection by a user, or by automatic process, of one or moremetrology target designs. The output may be hundreds, if not thousands,of metrology target designs. As discussed above, the metrology targetdesigns may also be associated with one or parameters of a metrologyrecipe, particularly where one or more metrology recipe parameters arevariable during simulation. The performance of the metrology targetdesign can be characterized by various parameters such as, for example,target coefficient (TC), stack sensitivity (SS), overlay impact (OV),asymmetry (as described herein), diffraction efficiency (as describedherein) or the like. Stack sensitivity can be understood as ameasurement of how much the intensity of the signal changes as overlaychanges because of diffraction between target (e.g., grating) layers.Target coefficient can be understood as a measurement of signal-to-noiseratio for a particular measurement time as a result of variations inphoton collection by the measurement system. In an embodiment, thetarget coefficient can also be thought of as the ratio of stacksensitivity to photon noise; that is, the signal (i.e., the stacksensitivity) may be divided by a measurement of the photon noise todetermine the target coefficient. Overlay impact measures the change inoverlay error as a function of target design. Further, the performanceof the metrology target design can be characterized by its robustness tovariation, e.g., its sensitivity to variation of one or more processparameters.

At 515, one or more metrology target designs (and associated metrologyrecipe parameters, if applicable) from the plurality of metrology targetdesigns at 510 are manually, or by automated process, selected. At 515,one or more guides, restrictions or thresholds may be provided tofacilitate selection of one or more metrology target designs. Forexample, a manual or automated criteria may be selection of a certainnumber of highest ranked metrology target designs from 510. The rankingmay be based on a single performance parameter, on a combination ofperformance parameters, or a weighted combination of performanceparameters, etc. Another manual or automated criterion may be selectionof a metrology target design passing a certain threshold for aperformance parameter, optionally if those metrology target designs door do not pass another threshold. For example, the manual or automatedcriteria may be evaluation of metrology target designs against stacksensitivity in relation to target coefficient.

At 520, the selected one or more metrology target designs (andassociated metrology recipe parameters, if applicable) from 515 areoutput along with the specifications of the metrology target designs(and associated metrology recipe parameters, if applicable). Theselection may be 10-40 metrology target designs per layer.

At 530, an optical proximity correction process may be performed toconvert the metrology target design into a design for a patterningdevice (e.g., a mask). The fundamental metrology target design may notbe directly converted into a pattern of, or for, a patterning device andyield the designed metrology target on a substrate. Accordingly, variousoptical proximity correction techniques, such as serifs, biases,scattering bars, etc., may need to be added to the metrology targetdesign to create a metrology target design suitable for a patterningdevice. The output at 535 may be a metrology target design pattern for apatterning device in, e.g., GDS format for each metrology target design.

At 540, the one or more patterning device patterns of the metrologytarget designs may be inserted into the device pattern of the one ormore patterning devices for the device manufacturing process. The resultfrom this would include information 545 regarding the selected one ormore metrology target designs and locations of the patterns of theselected one or more metrology target designs in the device pattern ofthe one or more patterning devices for the device manufacturing process.

Referring to FIG. 6, details of an embodiment of processes 410 and 415are presented. Using information 545, one or more metrology recipes(typically a plurality of metrology recipes) for each of the selectedone or more metrology target designs are generated. As noted above, ametrology recipe comprises one or more parameters (and one or moreassociated values) associated with the metrology apparatus itself usedto measure the one or more metrology targets and/or the measurementprocess, such as one or more wavelengths of the measurement beam, one ormore types of polarization of the measurement beam, one or more doses ofthe measurement beam, one or more bandwidths of the measurement beam,one or more aperture settings on the inspection apparatus associatedwith the measurement beam, the alignment marks used to locate themeasurement beam on the target, the alignment scheme used, the samplingscheme, the layout of the metrology targets and the movement scheme tomeasure the targets and/or points of interest of a target, etc.

To enable generation of the one or more metrology recipes, metrologyrecipe template information 605 may be provided. The metrology recipetemplate information 605 may define generic details regarding one ormore parameters of a metrology recipe such as alignment marks used tolocate the measurement beam on the target, the alignment scheme used,the size of the measurement beam spot, sampling schemes, etc.

At 610, a metrology recipe optimization process is performed todetermine one or more suitable metrology recipes for each metrologytarget design. To do so, measurements results 615 from one or moresubstrates patterned with the one or more metrology target designs andmeasured at the one or more generated metrology recipes may be analyzed.In an embodiment, such results are from a select number of targetsexposed on a substrate (i.e., a sample of the targets). One or moreperformance parameters may be calculated for combinations of metrologyrecipe and metrology target design and evaluated to determine which oneor more metrology recipes are most suitable. Results information, e.g.,optimization performance results, may be generated at 620.

At 625, a total measurement uncertainty (TMU) of the one or moremetrology target designs using one or more selected metrology recipesfrom 610 is determined. To do so, measurements results 630 from one ormore substrates patterned with the one or more metrology target designsand measured at the one or more selected metrology recipes may beanalyzed. In an embodiment, such results are from a select number oftargets exposed on a substrate (i.e., a sample of the targets). In anembodiment, any combinations of metrology target design and selectedmetrology recipe that equal or exceeds a threshold value of TMU may beruled out for further evaluation. Results information, e.g., TMUverification results, may be generated at 635.

At 640, the accuracy (e.g., by use of a residual) of one or more of themetrology target designs is determined. In an embodiment, the one ormore metrology target designs and their one or more associated metrologyrecipes that have sufficient TMU from 625 are analyzed. To determine theaccuracy, measurements results 645 from one or more substrates patternedwith those one or more metrology target designs and measured at theirassociated one or more metrology recipes may be analyzed. In anembodiment, such results are from all, nearly all, or at least themajority, of targets exposed on a substrate. In an embodiment, suchresults are from less than the majority of targets exposed on asubstrate where, for example, an appropriate sampling scheme is used.From the measurement results, the accuracy of the metrology targetdesigns may be evaluated by computing a residual between the measurementresults and a parameterized measurement data mathematical model used todescribe the measurement results. Those metrology target designs with alow residual are those that are more accurate. Information, e.g.,accuracy performance results and optionally inspection apparatuscorrections to reduce or minimize the residual, may be generated at 620.Further, correction settings for the inspection apparatus for use duringprocess control may be determined at 650.

In an embodiment, the process 625 may be performed after process 640.

At 655, the one or more metrology target designs along with their one ormore metrology recipes are evaluated to identify a subset of metrologytarget designs suitable for further evaluation. The evaluation may beperformed on the results from process 610, 625, 640 or any combinationselected therefrom. For example, a ranking by, or measure of,performance of the evaluated combinations of metrology target design andmetrology recipe may be created to allow selection by a user, or byautomatic process, of one or more metrology target designs (and itsassociated metrology recipe) from the evaluated combinations ofmetrology target design and metrology recipe.

At 660, a list of selected one or more metrology target designs aregenerated, which list may include the details of the one or moremetrology target designs and details of the associated one or moremetrology recipes. Where metrology targets are measured with only asingle inspection apparatus, the list may be ready for use in HVM,particularly where the inspection apparatus used is one used in HVM.

Referring to FIG. 7, details of an embodiment of process 420 arepresented where, e.g., more than one inspection apparatus is used tomeasure the one or more metrology targets in HVM and/or the inspectionapparatus for evaluation is different from that used in HVM. From thedata from 660, one or more combination of metrology target design andmetrology recipe are selected. For each combination, the metrologytarget is patterned onto a substrate and then measured with aninspection apparatus using the metrology recipe. In this case, eachcombination is measured using a first inspection apparatus at 700,measured using a second inspection apparatus at 705, and measured usinga third inspection apparatus at 710. In this example, there are threeinspection apparatuses, but there may be more or there may be less. Fromthe measurement results, an applicable correction 715, 720, 725 for therespective inspection apparatus may be determined, e.g., to reduce orminimize a residual. Further, at 730, the results from 700, 705, 710,results from 715, 720, 725, and/or performance parameters derived fromany of the foregoing may be evaluated to determine matching performancebetween the inspection apparatuses. For example, if one or morecombinations of metrology target design and metrology recipe performbetter on the inspection apparatuses collectively than one or more othercombinations then those combinations may be selected for HVM.

At 735, a list of selected one or more metrology target designs aregenerated for, e.g., HVM or for development of the manufacturingprocess, which list may include the details of the one or more metrologytarget designs and details of the associated one or more metrologyrecipes.

Referring to FIG. 8, a schematic flow diagram is depicted of anembodiment of metrology target design, selection and qualification. Inthis diagram, certain aspects of the flow are separated into generalcategories. A first category 800 of operations involves the design andselection of one or more metrology target designs by calculation orsimulation. This roughly corresponds to the metrology target design 405and all or parts of the process of FIG. 5, such as processes 500, 510,520 and 525. A second category 805 of operations involves data analysisassociated with of one of more of the metrology target designs selectedin category 800 to select one or more metrology target designs for HVM.And, a third category 810 of operations involves collection of data foruse in the one or more of the category 800 and/or 805 operations.

So, at 815, simulation steps as, for example, described above in respectmetrology target design 405 and all or parts of the process of FIG. 5,such as processes 500, 510, 520 and 525 are performed, using variousparameters including stack or other process conditions (e.g.,information regarding material, dimensional and/or opticalcharacteristics of the layer in which a metrology target, or portionthereof, is provided (such as an optical property, a material thickness,refractive index, absorption index, etc.), regarding one or more layersabove that metrology target (e.g., thickness of a processing layer,refractive index of a processing layer, absorption index of a processinglayer, etc.), regarding how a layer is processed (e.g., a polishingparameter, an etching parameter, etc.), regarding a characteristic of aninspection apparatus (as described further hereafter), regarding asetting of an inspection apparatus, regarding a characteristic of alithographic apparatus, regarding an alignment strategy to measure thetarget, etc. and/or a measure of variation of any of the foregoing), tosimulate performance of one or more different metrology target designs,which different metrology target designs may be created by thesimulation by varying one or more metrology target design parameters(such as periodic structure pitch, a structural feature criticaldimension, etc. and including one or more stack or other processconditions). As discussed above, the performance may be, and aperformance parameter may represent, printability, detectability,precision, robustness, throughput, accuracy, asymmetry, diffractionefficiency (as described hereafter), inspection tool specific parameter(e.g., sensitivity to sensor artifacts as described hereafter), etc. ora combination thereof.

The metrology target designs may be ranked or otherwise evaluated basedon their simulated performance (which is at nominal stack information).In an embodiment, the simulation is performed at a range of stack orother processing conditions around an expected or, as describedhereafter, a measured processing condition. The range may be defined bya user.

As described above, the simulation may be performed using variousdifferent metrology recipe parameters (e.g., different measurement beamwavelength, different measurement beam polarization, differentmeasurement beam dose, etc. or any combination thereof) and differentvalues thereof. Thus, the results may be a combination of metrologytarget design and one or more metrology recipe parameters (andassociated values) that, e.g., rank highly, pass a threshold, etc.

From the simulation, one or more of the metrology target designs may beselected to provide an initial set of metrology target designs. Thesemetrology target designs are output at 817. The data at 817 may furtherinclude the stack information, the simulated performance of themetrology target designs, their ranking and/or specification of one ormore associated metrology recipe parameters.

At 820, based on the data of 817, software generates one or moremetrology recipes (typically a plurality of metrology recipes) for oneor more, if not all, of the metrology target designs at 817 formetrology target design performance evaluation. This step generallycorresponds to step 600 described above. In an embodiment, the metrologyrecipes comprise combinations of all specific wavelengths andpolarizations available at the inspection apparatus. In an embodiment,the one or more metrology recipes for a particular metrology targetdesign comprise one or more of the associated metrology recipeparameters (and associated value(s) thereof) from data 817. In anembodiment, the one or more metrology recipes for a particular metrologytarget design may comprise a range of values around or with respect tothe value(s) of the one or more of the associated metrology recipeparameters from data 817. For example, if data 817 specifies ameasurement beam wavelength then the one or more metrology recipes mayinclude those with that measurement beam wavelength and/or in a rangearound or with respect to that measurement beam wavelength (e.g., arange of 50, 100, 150, 200, 250, 300 or 350 nm). The recipes are outputat 822.

At 825, the metrology target designs for which recipes are generated at820 are formed onto a plurality of substrates processed using the devicemanufacturing process and then measured with an inspection apparatususing the recipes of 822. This step generally corresponds to step 615.As discussed above in respect of step 615, the data collection may be asample of the targets on a substrate to aid speed of evaluation. In anembodiment, a programmed variation to a measured or derived parametermay be introduced. For example, where the measurements relate tooverlay, a known programmed overlay error may be introduced to helpperformance evaluation. The output 827 would be, e.g., overlay data foreach of a plurality of metrology target designs. And for each metrologytarget design, there would be data for a plurality of recipes. In anembodiment, the data may represent measured values or parameters derivedfrom measured values for one or more various metrology target designparameters and/or one or more various metrology recipe parameters. In anembodiment, the data collected at 825 may be data used to determine aparameter representative of sensitivity of one or more metrologyrecipes, or one or more metrology recipe parameters, to one or moremetrology targets.

In an embodiment, measurements may be performed of a structure (e.g., aperiodic structure) of a metrology target design to determine aparameter representative of variation of the structure due to processvariability. For example, the structure may have an asymmetry due tovariability in processing of the structure and/or one or more layersabove the structure. In an embodiment, to obtain such measurements,specific markers or features may be used to measure such variation. Suchspecific markers or features may also be used to monitor the devicemanufacturing process. In an embodiment, where the metrology targetdesign comprises a lower periodic structure and an upper periodicstructure, the measurements may be performed of a lower periodicstructure of a metrology target design without an associated upperperiodic structure of a metrology target design being located over thelower periodic structure at the time of measurement.

Thus, these measurements can represent a process variation arising inthe creation of the structure of the metrology target and/or of one ormore layers overlying the structure (and can be then be used to arriveat a robustness of a metrology target design to process variability).For example, these measurements can represent an amount of asymmetrypresent in the structure, e.g., the lower periodic structure of ametrology target design having an upper periodic structure. For example,low asymmetry can represent a robust target or target parameter. Forexample, a set of data may represent values of asymmetry for differentcombinations of wavelength and polarization for each of a plurality ofmetrology target designs. Such data, for example, may represent, or beused to derive, a parameter representative of sensitivity of one or moremetrology recipes, or one or more metrology recipe parameters, to one ormore metrology targets since such data show how different recipesmeasure a same target. As another example, a set of data may representvalues of asymmetry for different values of metrology target designparameter, such as pitch of a periodic structure of metrology targetdesigns, a critical dimension of a structural feature of metrologytarget designs, segmentation of features of a periodic structure ofmetrology target designs, etc. As another example, a set of data mayrepresent measured intensities for various metrology target designparameter or metrology recipe parameter.

Additionally, the measurements may be taken at different stages of thedevice manufacturing process to determine which process steps are likelycausing variability of the results, e.g., causing deformation of thestructure of the metrology target. That is, in an embodiment, theasymmetry (as an example) may be measured after each layer, or after acertain number of layers, of the stack is applied to investigate whichof the layers in the device manufacturing process causes the asymmetryto occur. This allows a layer by layer analysis of the stack, which canbe used for the tuning as described herein.

In an embodiment, one or more properties may be varied at one or more ofthese different stages to help determine if a metrology target design isrobust to variation of the one or more properties. The one or moreproperties may comprise one or more selected from: an optical propertyof a layer (e.g., a material refractive index or a material absorptionindex), a material thickness, a polishing parameter and/or an etchingparameter.

At 830, the data 827 is evaluated to filter combinations of metrologytarget design and recipes based on performance. This step generallycorresponds to step 610 and optionally 625. For example, the data 827 isprocessed to determine one or more parameters regarding the performanceof the metrology target designs and/or the metrology recipes. In anembodiment, the software generates one or more performance parametersregarding detectability, precision, throughput and/or accuracy. Based onmetrology target performance information from data 827 (e.g., the dataitself and/or a generated performance parameter), one or more metrologytarget designs and associated one or more metrology recipes aremanually, or by automated process, selected. In an embodiment,additionally or alternatively to selecting based on the metrology targetperformance information from data 827, the one or more metrology targetdesigns and associated one or more metrology recipes are manually, or byautomated process, selected based on data (such as a parameterrepresenting performance of one or more of the metrology targets and/ormetrology recipes) from the simulation 815 (e.g., obtained from 817and/or 819). In an embodiment, the selecting is based on metrologytarget performance information from data 827 and on data from thesimulation at 815. In an embodiment, the simulation is performed basedon a tuning of the metrology target parameter or metrology recipeparameter as described hereafter and the selecting is based on data fromthe simulation at 815 that is based on the tuning of the metrologytarget parameter or metrology recipe parameter. In an embodiment, thesimulation is performed based on a tuning of the metrology targetparameter or metrology recipe parameter as described hereafter and thesimulation evaluates one or more new or varied metrology targets and/ormetrology recipes. In an embodiment, measurement data of the one or morenew or varied metrology targets and/or metrology recipes is obtained andthe selecting is based on measurement data of the one or more new orvaried metrology targets and/or metrology recipes (in addition oralternatively to being based on data from the simulation at 815).

In an embodiment, combinations of metrology target design and metrologyrecipe are ranked according to one or more performance parametersindividually (which performance parameters themselves may be derivedfrom a plurality of performance parameters, e.g., a weighted combinationof performance parameters) and/or according to combinations ofperformance parameters (e.g., ranked separately on two or moreperformance parameters or ranked based on a combination of two or moreperformance parameters). In an embodiment, the ranking of combinationsof metrology target design and metrology recipe may be presented in auser interface (e.g., a graphical user interface). In an embodiment, oneor more combinations of metrology target design and metrology recipe maybe automatically selected if they pass a threshold. These promisingmetrology target designs and metrology recipes can then be analyzed, asdiscussed herein, for accuracy validation. The selected metrology targetdesigns and metrology recipes, and optionally their performance, areoutput at 832.

In an embodiment, a parameter representative of sensitivity of one ormore metrology recipes, or one or more metrology recipe parameters, toone or more metrology targets, such as a parameter representingvariation of a structure of the metrology target due to processvariability (e.g., derived from measurements performed of a lowerperiodic structure of a metrology target design without an associatedupper periodic structure of a metrology target design being located overthe lower periodic structure at the time of measurement), arefed-forward at 827 for use in the evaluation process of completemetrology target design. In an embodiment, the measurements are used todetermine which one or more measurements settings have a high or lowsensitivity to process variation arising in the creation of thestructure of the metrology target and/or of one or more layers overlyingthe structure. Thus, in an embodiment, the measurements are used todetermine which one or more measurements settings have a high or lowsensitivity to deformation of the structure, e.g., periodic structureasymmetry. These results can then be used in evaluation of the completemetrology target design at 830 to identify and/or select one or moremetrology target designs that have one or more low or least sensitivesettings. In an embodiment, the results may be fed-forward at 829 tocreation of the metrology recipes such that metrology recipes areselected that have one or more low or least sensitive settings, whichcan facilitate throughput by eliminating metrology recipes that arehighly sensitive to process variation.

In an embodiment, there is provided a method comprising: determining aparameter representative of sensitivity of one or more metrologyrecipes, or one or more metrology recipe parameters, to one or moremetrology targets based on measurement data of a metrology targetmeasured at a plurality of metrology recipes; and evaluating, based onthe parameter representative of sensitivity, a plurality of metrologyrecipes used to measure the metrology target by simulation or againstmeasured data to identify one or more recipes of the plurality ofmetrology recipes for use in measuring the metrology target. In anembodiment, the measurement data includes a parameter representingvariation of a structure of the metrology target due to processvariability. In an embodiment, the parameter represents a measure ofasymmetry present in the structure of the metrology target. In anembodiment, the measurement data comprises measurements at differentstages of processing of the structure and/or applying of layers abovethe structure. In an embodiment, the method further comprises varying aproperty of the processing of the structure. In an embodiment, theproperty of the processing comprises one or more selected from: anoptical property of a layer, a material thickness, a polishing parameterand/or an etching parameter. In an embodiment, the structure of themetrology target is a lower periodic structure of the metrology targetand the measurement data relates to the lower periodic structure withoutan upper periodic structure of the metrology target being located abovethe lower periodic structure at the time of acquisition of themeasurement data.

At 834, feedback data from or, or generated from, the measurement datagathered at 825 is provided back to the simulation or calculationprocess at 800. This data can be used to verify the simulations,simulation parameters, and/or give simulation confidence. Thus, in anembodiment, the data is used to tune a metrology target parameter and/ormetrology recipe parameter derived or used in the simulation.

In an embodiment, the data 834 may be, or comprises, values of one ormore parameters of the stack, e.g., the thickness of one or more layers,the refractive index of one or more layers, the absorption index of oneor more layers, etc., and/or a variability of one or more parametersregarding the stack, e.g., a measure of variability of thickness of oneor more layers. This tuning may be of one or more layers at or above thetarget and/or one or more layers underneath the target. Such data 834may be measured directly by a metrology tool. Such data 834 may begathered by a metrology tool that is not designed to use the target,e.g., by a CD-SEM tool whereas the target is designed for use by adiffraction-based measurement tool.

In an embodiment, the data 834 may be, or comprise, indirect informationregarding a metrology target parameter and/or metrology recipeparameter. For example, the data 834 may comprise values of measuredintensities of radiation redirected by the measured metrology targetdesigns, measured values of overlay, measured values of criticaldimension, values of one or more parameters (KPIs) such as mean,standard deviation, stack sensitivity, target coefficient, asymmetry,diffraction efficiency, etc. derived from the measurement data, etc. Inan embodiment, the data 834 may comprise measured data, or one or moreparameters derived from measured data, that represent reproducibility ofthe metrology target design (i.e., an indicator of the ability of themetrology design to be actually produced in the stack as designed)and/or detectability (i.e., an indicator of the ability of an inspectionapparatus to detect the metrology design).

At 840, this feedback data may be used to evaluate the correctnessand/or consistency of one or more metrology target parameters and/ormetrology recipe parameters of the simulation and an appropriatecorrection may be applied where there is lack of correctness and/orconsistency. For example, one or more of the initial or expected stackor other process conditions used to run the simulation may be verifiedagainst the data 834 to verify the validity of the one or more initialor expected stack or other process conditions. If the one or moreinitial or expected stack or other process conditions is not valid(e.g., values of numbers do not match, variability of a parameter isgreater than as used in the simulation, etc.), the simulation may bere-run using updated one or more stack or other process conditionssupplied at 842. For example, one or more measured stack or otherprocess conditions from the feedback data may be used in the simulationinstead of the one or more of the initial or expected stack or otherprocess conditions. The re-performance of the simulation may involvemerely re-ranking of previously determined metrology target designsand/or metrology recipes based on the updated one or more stack or otherprocess conditions or may involve determining one or more new metrologytarget designs and/or metrology recipes based on the updated one or morestack or other process conditions. Verification may range from simplecomparison of numbers to complex statistical analysis. For example,measurement detectability of a metrology target design may be evaluatedbased on measurements of the metrology target design for a plurality ofvalues of a metrology recipe parameter or for a plurality of metrologyrecipe parameter combinations. This may yield a set of data, orfunction, of measurement detectability against values of the metrologyrecipe parameter or of the plurality of metrology recipe parametercombinations. A comparable set of data, or function, may be derived fromthe simulation and then statistically compared. If there is no accuracyor consistency, a correction may be applied to the simulation. In anembodiment, the simulation may vary one or more metrology targetparameters and/or metrology recipe parameters (such as one or moreparameters of the stack) until there is a match with data 834 and thenapply a correction based on that result. As an example, the simulationmay vary one or more parameters of the stack until there is a match withdata 834 and the values of the one or more parameters of the stack inthe simulation at the time of match may be representative of the actualstack characteristics. The one or more parameters of the stack in thesimulation at the time of match may then be used in subsequentsimulations for that device manufacturing process. In an embodiment,measurements of critical dimension may be used to constrain the stacktuning and to get a better (physical) solution of the tuned stack.

Relatedly, if measurements are consistent with or confirm the accuracyof one or more metrology target parameters and/or metrology recipeparameters of the simulation, the simulation can use this information842 to improve or optimize the metrology target design and/or metrologyrecipe. For example, strong correlations may be identified betweenparameters and used to guide the design of metrology target designsand/or metrology recipes to favor those parameters with strongcorrelation to parameters that represent good performance. For example,if measurement results of multiple metrology target designs (withvarying metrology target design parameters) for, for example, aplurality of, or one or more applicable, metrology recipe parameters areconsistent with or confirm the accuracy of one or more metrology targetparameters and/or metrology recipe parameters of the simulation, thenthat information can be used by the simulation to improve or optimizethe metrology target design and/or metrology recipe (e.g., by giving agreater weight to parameters with a stronger correlation to betterperformance, etc.).

In an embodiment, where correlation results between measured data andinitial data in 840 flags one or more parameters of the stack and/or avariability of one or more parameters regarding the stack to beincorrect, measurements may be taken to obtain values of one or moreparameters of the stack and/or a variability of one or more parametersregarding the stack. For example, such data may be collected at 825 andtriggered to be collected responsive to 840 determining that one or moreparameters of the stack and/or a variability of one or more parametersregarding the stack are incorrect. The initial data may be updated basedon such data or be substituted with such data. From the correlation at840, step 840 may determine specific one or more parameters of the stackand/or a variability of one or more parameters regarding the stack to bemeasured at 825. In an embodiment, step 840 may automatically prepare orprovide a metrology recipe template for use 825 to measure the one ormore parameters of the stack and/or a variability of one or moreparameters regarding the stack that are determined to be incorrect.

In an embodiment, data 834 could be used as, or derived to be, a weightvalue used in the simulation to tune a metrology target parameter and/ormetrology recipe parameter. For example, the weight value couldeffectively be used to eliminate one or more metrology target designsand/or metrology target recipes. As an example, data 834 representingreproducibility or detectability may be used as a “heavy” weight to ruleout, or lower in rank, certain metrology target designs and/or metrologytarget recipes. The result could be faster simulation and more effectiveresults.

In an embodiment, if a difference between one or more initial orexpected stack or other process conditions or expected data andrespectively one or more of the measured stack or other processconditions or the measured data remains within a threshold, then one ormore metrology targets and/or recipes may be selected based onperformance. In an embodiment, the performance is determined using aperformance parameter or indicator comprising one or more selected from:detectability, precision, throughput, accuracy, diffraction efficiency,asymmetry, target coefficient, stack sensitivity, and/or sensitivity tosensor artifacts. In an embodiment, the selection is based on a balancebetween several performance parameters and/or a balance between aperformance parameter and an inspection apparatus specific parameter.

In an embodiment, the feedback data used for consistency and/or accuracyevaluation may be feedback data that corresponds to one or moreparticular simulated metrology target designs and/or metrology recipes(e.g., measured data of a particular metrology design is used to tuneone or more parameters of the simulation of that particular metrologydesign). Thus, in an embodiment, only specific metrology target designsand/or specific metrology recipes may be evaluated during a re-run ofthe simulation based on data 834. This may be accomplished using, e.g.,a weight factor (such as one based on data 834 representative ofreproducibility or detectability). In an embodiment, the feedback dataused for consistency and/or accuracy evaluation may be general to aplurality of metrology target designs and/or metrology recipes.

In an embodiment, the tuning of the metrology target parameter ormetrology recipe parameter makes a particular metrology target and/ormetrology recipe more robust to variation in the process of forming ormeasuring the particular metrology target, to variation in the processof forming the metrology target used with the particular metrologyrecipe, or to variation in the process of measuring using the particularmetrology recipe. For example, in an embodiment, measurementsrepresenting variation of a structure of the metrology target due toprocess variability (such as measurements performed of a lower periodicstructure of a metrology target design without an associated upperperiodic structure of a metrology target design being located over thelower periodic structure at the time of measurement) is used as, or usedto derive, feedback data 834. The feedback data 834 can then represent aprocess variation arising in the creation of the structure of themetrology target and/or of one or more layers overlying the structure,which can then be used to arrive at a robustness of a metrology targetdesign and/or metrology recipe to process variability. For example,feedback data 834 indicating low asymmetry indicates that the metrologytarget design and/or metrology recipe is robust to process variation.The feedback data 834 may, for example, represent a set of data, orfunction, of asymmetry against values of metrology target design pitch,measurement beam wavelength, etc. And so, the feedback data 834 may beused in the simulation to design and/or select metrology target designsand/or metrology recipes having one or more parameters that showrobustness. The feedback data 834 may further represent different stagesof the device manufacturing process and thus may be applied to theappropriate parts of the simulation. Thus, this feedback data 834 may beused in the simulation to identify one or more parameters which can betuned to make a more robust metrology target design and/or metrologyrecipe.

In an embodiment, the simulation process 815 may be re-run responsive tofeedback or feed-forward data. In an embodiment, if a difference betweenone or more initial or expected stack or other process conditions orexpected data and respectively one or more of the measured stack orother process conditions or the measured data crosses a threshold, thesimulation may be re-performed using a variation of the initial orexpected stack or other process conditions (e.g., using the one or moreof the measured stack or other process conditions) as well asre-performing the identifying of the one or more metrology targetdesigns and/or metrology recipes from those simulated.

In an embodiment, when the simulation process 815 is re-run, the processmay proceed from simulation process 815 onto the metrology recipeformulation at 820 and so forth. For example, this may be particularlythe case where the feedback or feed-forward data would yield a changedor new metrology target design that should be measured at 825. In anembodiment, responsive to feedback or feed-forward data, the process mayproceed via 819 to the evaluation process at 830. For example, this maybe particularly the case where there is no changed or new metrologytarget design that should be measured. Data may be supplied via 819 toaid in selection of one or more metrology target designs and/ormetrology recipes. For example, the data may include revised ranking ofone or more metrology target designs and/or metrology recipes originallysupplied via 817 and/or new values of performance parameters associatedwith one or more metrology target designs and/or metrology recipesoriginally supplied via 817. The ranking and/or revised or new valuesmay be used at process 830 in the selection of one or more metrologytarget designs and/or metrology recipes.

At 835, the one or more selected metrology target designs at 830 areformed onto a plurality of substrates processed using the devicemanufacturing process and then measured with an inspection apparatususing their associated one or more metrology recipes for accuracyvalidation. This step generally corresponds to step 645. As discussedabove in respect of step 645, the data collection may be a morecomprehensive analysis of all, substantially all or a majority of thetargets on a substrate. In an embodiment, a programmed variation to ameasured or derived parameter may be introduced. For example, where themeasurements relate to overlay, a known programmed overlay error may beintroduced to help performance evaluation. The output 837 would be,e.g., overlay data for each of the plurality of metrology targetdesigns. And for each metrology target design, there would be data forthe plurality of recipes. In an embodiment, the data may representmeasured values or parameters derived from measured values for one ormore various metrology target design parameters and/or one or morevarious metrology recipe parameters. In an embodiment, measurements maybe performed to determine variation of a structure (e.g., a periodicstructure) of the metrology target due to process variability. As anon-limiting example, such measurements may be of a lower periodicstructure of a metrology target design without an associated upperperiodic structure of a metrology target design being located over thelower periodic structure. These measurements may represent, for example,an amount of asymmetry present in the structure and can be then be usedto arrive at a robustness of a metrology target design to processvariability. For example, low asymmetry can represent a robust target ortarget parameter. For example, a set of data may represent values ofasymmetry for different combinations of wavelength and polarization foreach of a plurality of metrology target designs. As another example, aset of data may represent values of asymmetry for different values ofmetrology target design parameter, such as pitch of a periodic structureof metrology target designs, a critical dimension of a structuralfeature of metrology target designs, segmentation of features of aperiodic structure of metrology target designs, etc. As another example,a set of data may represent measured intensities for various metrologytarget design parameter or metrology recipe parameter. Additionally, themeasurements may be taken at different stages of the devicemanufacturing process to determine which process steps are likelycausing deformation of the structure.

Based on the data 837, one or more performance indicators regarding theone or more selected metrology target designs and associated one or moremetrology recipes measured at 830 are calculated at 845. This stepgenerally corresponds to step 640 and optionally step 625. For example,the data 837 is processed to determine one or more parameters regardingthe performance of the metrology target designs and/or the metrologyrecipes such as detectability, precision, throughput and/or accuracy. Inan embodiment, a parameter regarding accuracy performance is calculatedin respect of the metrology target design—metrology recipe combinations.In an embodiment, the accuracy performance parameter comprises aresidual between the measured data and a mathematical model used to fitthe measured data.

Based on the determined metrology target performance from data 837, oneor more metrology target designs and associated one or more metrologyrecipes are manually, or by automated process, selected. In anembodiment, combinations of metrology target design and metrology recipeare ranked according to one or more performance parameters individually(which performance parameters themselves may be derived from a pluralityof performance parameters, e.g., a weighted combination of performanceparameters) and/or according to combinations of performance parameters(e.g., ranked separately on two or more performance parameters or rankedbased on a combination of two or more performance parameters). In anembodiment, the ranking of combinations of metrology target design andmetrology recipe may be presented in a user interface (e.g., a graphicaluser interface). In an embodiment, one or more combinations of metrologytarget design and metrology recipe may be automatically selected if theypass a threshold. These metrology target designs and metrology recipesmay then represent the one or more metrology target design—metrologyrecipe combinations ready for consideration for HVM and so may be outputat 860, optionally with the associated performance. In an embodiment,the user or software may select one or more candidate “point ofreference” (POR) metrology target designs with, e.g., good targetperformance. The one or more POR metrology target designs and associatedmetrology recipe(s), and optionally associated performance, is output at847.

In an embodiment, the feedback and feed-forward described above (e.g.,steps 819, 827, 829, and/or 834) may be applied in association with step845.

At 850, the one or more POR metrology target designs at 845 are formedonto a plurality of substrates processed using the device manufacturingprocess and then measured with a plurality of inspection apparatusesusing the POR metrology target designs' associated one or more metrologyrecipes for inspection apparatus to inspection apparatus matching. Thisstep generally corresponds to steps 700, 705 and 710. As noted above,this data collection would apply if, for example, multiple inspectionapparatuses are used to measure metrology targets in the devicemanufacturing process or where a different inspection apparatus is usedfor development than in HVM. The data collection may be a morecomprehensive analysis of all, substantially all or a majority of thetargets on a substrate. The output 852 would be, e.g., overlay data foreach of the plurality of metrology target designs. And for eachmetrology target design, there would be data for the plurality ofinspection apparatuses.

Based on the data 852, an applicable correction for the respectiveinspection apparatus may be determined, e.g., to reduce or minimize aresidual at 855. Additionally or alternatively, matching performancebetween inspection apparatuses is evaluated at 855. For example, one ormore parameters may be derived from data 852 to evaluate matching ofperformance for a metrology target design—metrology recipe combinationacross each of the inspection apparatuses for optionally all or aplurality of layers of substrate. This step generally corresponds tosteps 715, 720, 725 and 730. For example, if one or more combinations ofmetrology target design and metrology recipe perform better on theinspection apparatuses collectively than one or more other combinationsthen those combinations may be selected for HVM. Based on the determinedmatching performance from data 837, one or more metrology target designsand associated one or more metrology recipes may be manually, or byautomated process, selected. In an embodiment, combinations of metrologytarget design and metrology recipe are ranked according to one or moreperformance parameters individually (which performance parametersthemselves may be derived from a plurality of performance parameters,e.g., a weighted combination of performance parameters) and/or accordingto combinations of performance parameters (e.g., ranked separately ontwo or more performance parameters or ranked based on a combination oftwo or more performance parameters). In an embodiment, the ranking ofcombinations of metrology target design and metrology recipe may bepresented in a user interface (e.g., a graphical user interface). In anembodiment, one or more combinations of metrology target design andmetrology recipe may be automatically selected if they pass a threshold.The selected one or more POR metrology target design—metrology recipecombinations may then represent the one or more metrology targetdesign—metrology recipe combinations ready for HVM and so may be outputat 860, optionally with the associated performance.

So, in an embodiment, there is provided a method comprising: performinga simulation to evaluate a plurality of metrology targets and/or aplurality of metrology recipes used to measure a metrology target;identifying one or more metrology targets and/or recipes from theevaluated plurality of metrology targets and/or recipes; receivingmeasurement data of the one or more identified metrology targets and/orrecipes; and using the measurement data to tune a metrology targetparameter and/or a metrology recipe parameter, of the simulation. In anembodiment, the tuning of the metrology target parameter or metrologyrecipe parameter makes an identified metrology target and/or recipe morerobust to variation in the process of forming or measuring theidentified metrology target, to variation in the process of forming themetrology target used with the identified recipe, or to variation in theprocess of measuring using the identified metrology recipe. In anembodiment, the measurement data comprises a parameter representingvariation of a structure of the metrology target due to processvariability. In an embodiment, the parameter represents a measure ofasymmetry present in the structure of the metrology target. In anembodiment, the measurement data comprises measurements at differentstages of processing of the structure and/or applying of layers abovethe structure. In an embodiment, the method further comprises varying aproperty of the processing of the structure. In an embodiment, theproperty of the processing comprises one or more selected from: anoptical property of a layer, a material thickness, a polishing parameterand/or an etching parameter. In an embodiment, the periodic structure ofthe metrology target is a lower periodic structure of the metrologytarget and the measurement data relates to the lower periodic structurewithout an upper periodic structure of the metrology target beinglocated above the lower periodic structure at the time of acquisition ofthe measurement data. In an embodiment, the measurement data comprisesmeasured sensitivity of a parameter of the metrology target tomeasurement beam wavelength. In an embodiment, the method furthercomprises using the measurement data to derive a parameter and using thederived parameter tune the metrology target parameter or metrologyrecipe parameter. In an embodiment, the derived parameter comprises oneor more selected from: overlay, stack sensitivity, target coefficient,asymmetry and/or diffraction efficiency. In an embodiment, the methodfurther comprises selecting, based on the measurement data, one or moremetrology targets and/or metrology recipes from the identified one ormore metrology targets and/or metrology recipes. In an embodiment, themethod further comprises performing the simulation based on the tuningof the metrology target parameter or metrology recipe parameter andre-selecting, based on measurement data of one or more identified new orvaried metrology targets and/or metrology recipes from the simulationand/or based on a performance parameter determined based on the tuningof the metrology target parameter or metrology recipe parameter, one ormore metrology targets and/or metrology recipes from identified one ormore metrology targets and/or metrology recipes. In an embodiment, there-selecting is based on the performance parameter and the performanceparameter comprises one or more selected from: overlay, stacksensitivity, target coefficient, asymmetry and/or diffractionefficiency.

In an embodiment, there is provided a method comprising: receivingmeasurement data of a plurality of different metrology targets, eachmeasured at a plurality of metrology recipes; and using the measurementdata to verify one or more parameters of a simulation used to evaluate aplurality of metrology targets and/or a plurality of metrology recipesused to measure a metrology target. In an embodiment, the method furthercomprises changing the one or more parameters based on the measurementdata. In an embodiment, the one or more parameters represent one or moreparameters of a process to form a metrology target. In an embodiment,the one or more parameters of a process to form a metrology targetcomprise one or more selected from: an optical property of a layer, amaterial thickness, a polishing parameter and/or an etching parameter.In an embodiment, the simulation uses the measurement data to optimize ametrology target and/or metrology recipe. In an embodiment, themeasurement data comprises measured sensitivity of a parameter of themetrology target to measurement beam wavelength. In an embodiment, themethod further comprises selecting, based on the measurement data, oneor more metrology targets and/or metrology recipes from the evaluatedone or more metrology targets and/or metrology recipes. In anembodiment, the method further comprises performing the simulation basedon the changed one or more parameters and re-selecting, based onmeasurement data of one or more evaluated new or varied metrologytargets and/or metrology recipes from the simulation and/or based on aperformance parameter determined based on the changed one or moreparameters, one or more metrology targets and/or metrology recipes fromevaluated one or more metrology targets and/or metrology recipes. In anembodiment, re-selecting is based on the performance parameter and theperformance parameter comprises one or more selected from: overlay,stack sensitivity, target coefficient, asymmetry and/or diffractionefficiency.

In an embodiment, there is provided a method comprising: simulating aplurality of metrology targets and/or a plurality of metrology recipestaking an expected process condition into account; identifying one ormore metrology targets and/or recipes from the simulated plurality ofmetrology targets and/or recipes; receiving measurement data of the oneor more identified metrology targets and/or recipes; and using themeasurement data to verify the expected process condition. In anembodiment, the method further comprises, if a difference between theexpected process condition or expected data and respectively a measuredprocess condition or the measured data crosses a threshold,re-performing the simulating using a variation of the expected processcondition and the identifying. In an embodiment, the simulating is doneat a range of processing conditions around the expected or measuredprocessing condition. In an embodiment, the range is defined by a user.In an embodiment, the metrology target comprises a lower target portionand comprises an upper target portion arranged in a layer between thelower target portion and an inspection apparatus configured to determinean overlay value between the upper and lower target portions. In anembodiment, receiving measurement data comprises receiving measurementdata only from the lower target portion. In an embodiment, the methodfurther comprises, if a difference between the expected processcondition or expected data and respectively a measured process conditionor the measured data remains within a threshold, selecting one or moremetrology targets and/or recipes based on performance. In an embodiment,the performance is determined using a performance indicator comprisingone or more selected from: detectability, precision, throughput,accuracy, diffraction efficiency, asymmetry and/or sensitivity to sensorartifacts. In an embodiment, the performance is a balance betweenseveral performance indicators and/or a balance between a performanceindicator and an inspection apparatus tool characteristic. In anembodiment, the inspection apparatus tool characteristic comprises aparameter representing sensitivity of inspection apparatus measurementsto sensor artifacts and/or straylight. In an embodiment, the processcondition comprises one or more selected from: an optical property of alayer, a material thickness, a polishing parameter, an etchingparameter, refractive index of a processing layer, absorption index of aprocessing layer, thickness of a processing layer, a variation in alayer, a characteristic of an inspection apparatus, a setting of aninspection apparatus, a measurement beam wavelength used by aninspection apparatus, a characteristic of a lithographic apparatus,and/or an alignment strategy.

In an embodiment, there is provided a method comprising: performing asimulation to evaluate a plurality of metrology targets and/or aplurality of metrology recipes used to measure a metrology target anddetermining a parameter representing performance of one or more of themetrology targets and/or metrology recipes; identifying one or moremetrology targets and/or metrology recipes from the evaluated pluralityof metrology targets and/or metrology recipes; receiving measurementdata of the one or more identified metrology targets and/or metrologyrecipes; and selecting, based on the measurement data and the parameter,one or more metrology targets and/or metrology recipes from theidentified one or more metrology targets and/or metrology recipes. In anembodiment, the method further comprises using the measurement data totune a metrology target parameter or metrology recipe parameter, of thesimulation, and performing the simulation based on the tuning of themetrology target parameter or metrology recipe parameter to determinethe parameter representing performance. In an embodiment, performing thesimulation based on the tuning of the metrology target parameter ormetrology recipe parameter comprises evaluating one or more new orvaried metrology targets and/or metrology recipes, the method furthercomprises receiving measurement data of the one or more new or variedmetrology targets and/or metrology recipes, and the selecting comprisesselecting based on the performance parameter and measurement data of theone or more new or varied metrology targets and/or metrology recipes. Inan embodiment, the parameter representing performance comprises one ormore selected from: overlay impact, stack sensitivity, process variationrobustness, target coefficient, asymmetry and/or diffraction efficiency.

In an embodiment, there is provided a method comprising: performing asimulation to evaluate a plurality of metrology targets and a pluralityof metrology recipes used to measure a metrology target; identifying oneor more combinations of metrology target and metrology recipe from theevaluated plurality of metrology targets and metrology recipes;formulating a plurality of metrology recipes for the one or moremetrology targets from the identified one or more combinations based onthe one or more metrology recipes from the identified one or morecombinations; and receiving measurement data of the one or moremetrology targets from the identified one or more combinations measuredusing the formulated plurality of metrology recipes. In an embodiment,the method further comprises selecting, based on the measurement data,one or more metrology targets from the one or more metrology targetsfrom the identified one or more combinations. In an embodiment, theformulated plurality of metrology recipes comprises one or moremetrology recipes from the identified one or more combinations. In anembodiment, the one or more metrology recipes from the identified one ormore combinations comprises a parameter and the formulated plurality ofmetrology recipes comprises metrology recipes having a value of theparameter within a certain range of values of the parameter of the oneor more metrology recipes from the identified one or more combinations.

In an embodiment, metrology target design/metrology target recipesimulation, evaluation and/or selection may take into accountdiffraction efficiency (DE), or a parameter derived from diffractionefficiency, as an additional or alternative parameter (e.g., as aranking parameter or as a calculation parameter (e.g., a multiplicationfactor)). The diffraction efficiency parameter represents a proportionof radiation redirected (e.g., diffracted) by the target toward thedetector. Thus, the diffraction efficiency may be used, for example, tohelp distinguish radiation that should be measured from stray radiationin the measurement process. A higher DE can mean, e.g., a shorterintegration time to arrive at a measurement. As another example, ahigher DE can mean less sensitivity to inspection apparatus sensorartefacts. So, for example, metrology target designs having comparabletarget coefficients but a metrology target design having the targetcoefficient at a higher DE is favored over a metrology target designhaving the target coefficient at a lower DE. In an embodiment, athreshold may be associated with the diffraction efficiency parameter,e.g., a threshold above which the diffraction efficiency must exceed.

So, in an embodiment, there is provided a method comprising: evaluatinga plurality of metrology targets and/or a plurality of metrology recipesused to measure a metrology target by simulation or against measureddata; and identifying one or more metrology targets and/or recipes fromthe evaluated plurality of metrology targets and/or recipes for whichdiffraction efficiency, or a parameter derived from diffractionefficiency, crosses a threshold. In an embodiment, the metrology recipescomprise a measurement beam wavelength and/or measurement beampolarization.

In an embodiment, metrology target design/metrology target recipesimulation, evaluation and/or selection may take into account aninspection apparatus specific parameter, or a parameter derived from theinspection apparatus specific parameter, as an additional or alternativeparameter (e.g., as a ranking parameter or as a calculation parameter(e.g., a multiplication factor)). The inspection apparatus specificparameter may be specific to an individual inspection apparatus, to aspecific group of individual inspection apparatuses, or to a type ofinspection apparatus. The inspection apparatus specific parameterdistinguishes from generic parameters applicable to inspection (and thusgenerally all inspection apparatus) such as wavelength choice,polarization choice, etc. But, the inspection apparatus specificparameter may be a variability associated with one or more such genericparameters that is inspection apparatus specific. In an embodiment, theinspection apparatus specific parameter comprises a measurement beamwavelength dependency of an inspection apparatus. In an embodiment, theinspection apparatus specific property comprises a parameterrepresenting sensitivity of inspection apparatus measurements to sensorartifacts and/or straylight. In an embodiment, the inspection apparatusspecific property comprises a characteristic or sensitivity of a sensorof an inspection apparatus. In an embodiment, the inspection apparatusspecific parameter comprises a parameter representing dependency ofinspection apparatus artefacts or straylight on measurement beamwavelength. Such a parameter may involve a mathematical function orcollection of data that represents the dependency of inspectionapparatus artefacts on measurement beam wavelength. In an embodiment,the function or collection of data may be a representation of inspectionapparatus sensor background noise or intensity as a function ofmeasurement beam wavelength values. In general, an inspection apparatusmay have a higher amount of sensor artefacts at a higher measurementbeam wavelength. So, for example, metrology target designs havingcomparable stack sensitivities but a metrology target design having thestack sensitivity at a lower measurement beam wavelength is favored overa metrology target design having the stack sensitivity at a highermeasurement beam wavelength. In an embodiment, a threshold may beassociated with the inspection apparatus specific parameter, e.g., athreshold above which the inspection apparatus specific parameter shouldor must exceed or should or must remain below (e.g., where the parameterrepresents dependency of inspection apparatus artefacts on measurementbeam wavelength, the threshold may be a measurement beam wavelengthlimit).

So, in an embodiment, there is provided a method comprising: evaluatinga plurality of metrology targets and/or a plurality of metrology recipesused to measure a metrology target by simulation or against measureddata; and identifying one or more metrology targets and/or recipes fromthe evaluated plurality of metrology targets and/or recipes for which ameasurement apparatus property, or a parameter derived from themeasurement apparatus property, crosses a threshold. In an embodiment,the measurement apparatus property comprises a measurement beamwavelength dependency of a measurement apparatus. In an embodiment, themeasurement apparatus property comprises a multiplication factorassociated with measurement beam wavelength dependency of a measurementapparatus. In an embodiment, the measurement apparatus propertycomprises a function or data representing background intensity of ameasurement apparatus against measurement beam wavelength. In anembodiment, the metrology recipes comprise a measurement beam wavelengthand/or measurement beam polarization. In an embodiment, the measurementapparatus property comprises a characteristic or sensitivity of a sensorof a measurement apparatus. In an embodiment, the measurement apparatusproperty comprises a dependency of straylight or sensor artifacts of aninspection apparatus on measurement beam wavelength.

Once the one or more metrology target designs and associated one or moremetrology recipes have been selected for HVM, the metrology process isconfigured to enable measuring of the one or more metrology targets onsubstrates for monitoring and control of the device manufacturingprocess. This was generally described in respect of step 340. As notedabove, it may be too time consuming to measure every metrology targetfor every substrate of every lot. Further, it is possible to model themeasurement results of the metrology targets using one or moremeasurement data mathematical models that are appropriatelyparameterized (i.e., mathematical models with appropriately decided anddefined parameters, and values thereof as applicable, to fit the data,e.g., to mathematically specify and model the data). So, a measurementdata mathematical model and/or measurement sampling scheme may beestablished for measuring the one or more metrology targets.

Thus, in an embodiment, there is provided an application that based onmeasurements of exposed substrates determines one or more settings forsubstrates that are subsequently being exposed. But, measurements areinevitably uncertain (e.g., contaminated with noise) and/or areinevitably not completely fitted by a mathematical model. Further, inthe flow from measurements on previous substrates to settings for thefuture substrates, other sources of uncertainty can be present. Further,there may be systematic variation in measured data. So, there isprovided a method to account for systematic variation and uncertainty toarrive at settings that can reduce uncertainty.

FIG. 9 schematically depicts a flow diagram of an embodiment ofmeasurement data mathematical model and sampling scheme evaluation. Theanalysis in the method of FIG. 9 would typically be per layer and perdevice manufacturing process (including different device patterns usedin a device manufacturing process). In an embodiment, the method mayperform parallel processing if there are various different layers,device manufacturing processes, etc. under consideration.

At 900, various preparatory data is obtained and some optionalpreparatory data processing is performed. At 905, measurements resultsfrom one or more substrates (desirably a plurality of substrates)patterned with the one or more metrology target designs and measuredwith an inspection apparatus at their associated one or more metrologyrecipes is obtained or received. In an embodiment, such results are fromall, nearly all, or at least the majority, of targets exposed on asubstrate. In an embodiment, the measurement data is from one substratelot, which is densely measured. Using one lot helps avoid lot to lotvariation, although substrate-to-substrate variation within the lotremains. For example, in an embodiment, there may be data from more than2000 points on each substrate of a batch of 20 or more substrates. Thedata may be converted into a map corresponding to the layout of thesubstrate. In an embodiment, the measurement data comprises one or moreof: overlay data, overlay error data, alignment data, critical dimensiondata (e.g., critical dimension uniformity data), and/or focus data.

At 910, the measurement data from 905 may optionally be processed toback-out a correction that may have been applied in the inspectionapparatus used to measure the data from 905 and/or applied in a devicemanufacturing process used to process the substrates corresponding tothe data from 905.

At 920, one or more measurement data mathematical models are providedfor consideration, which one or more measurement data mathematicalmodels may be, for example, determined or specified for the measurementdata. For example, there may be a collection of measurement datamathematical models and each measurement data mathematical model may beevaluated as discussed hereafter. The mathematical models may define aset of basis functions that fit the data once parameterized. In anembodiment, one or more measurement data mathematical models of thecollection (which may be all the measurement mathematical data models inthe collection) may be determined by mathematical evaluation (e.g., the“fingerprint” of the data roughly or closely matches one or moremeasurement data mathematical models of the collection) to be a possiblefit (e.g., a relative close fit) for the data. In an embodiment, a usermay specify one or more measurement data mathematical models of thecollection for further consideration as discussed hereafter, whetherthat measurement data mathematical model was determined to be a fit ornot. For example, an interface (such as a graphical user interface) mayallow the user to specify the measurement mathematical data models forconsideration. In an embodiment, a plurality of measurement mathematicaldata models are determined or specified for further evaluation asdiscussed hereafter, desirably as many models as feasible that fit themeasurement data. In an embodiment, the mathematical model may be tunedto match the fingerprint for optimal noise suppression (e.g.,eliminating redundant orders or reducing the use of higher orders).

At 925, one or more inspection apparatus throughput models arespecified. In an embodiment, the inspection apparatus throughput modelspecifies, for example, the number of substrates measured per unit time,number of targets or points measured per unit of time or other metricrepresenting throughput of measurement of targets on substrates. In anembodiment, the inspection throughput model may specify the location oftargets on a substrate and/or distances between targets, the measurementfield size, the number of points on a target to be measured, substrateand/or beam scanning speed, a loading time of a substrate in theinspection apparatus, an alignment time of the substrate in theinspection apparatus, a reposition time of the substrate in theinspection apparatus, a time for positioning a measurement target withina measurement position in the inspection apparatus, a time to retrievethe measurement data from a measurement target in the inspectionapparatus, etc., which data may be used to arrive at a measurementthroughput. The inspection apparatus throughput model may be a complexmathematical formula that will be permit variables to be changed asdescribed further. In an embodiment, a user may specify a throughputthreshold, e.g., a certain minimum throughput that is desired. In anembodiment, a plurality of inspection apparatus throughput models, eachrepresenting a different inspection apparatus, are specified for furtherevaluation as discussed hereafter. In an embodiment, the mathematicalmodel may be configurable by a user in terms of parameters to use in thefit. For example, the user may be presented with one or more basemathematical models and can select or constrain which one or moreparameters of those one or more base mathematical models are used in afit. In an embodiment, the mathematical model may be parameterized forspecific features or devices of the device manufacturing process. Forexample, a mathematical model may be parameterized for a specificsubstrate table (e.g., in a lithographic apparatus) of a plurality ofsubstrate tables. As a further example, a mathematical model may beparameterized for a particular substrate movement direction duringexposure (e.g., scan direction).

At 930, one or more sampling schemes for a metrology process aredetermined for further evaluation as discussed hereafter. In anembodiment, a sampling scheme may include one or more parametersselected from: number of sample points per substrate, number ofsubstrates per lot sampled; numeric designation of the substrate(s) in alot or per lot sampled; number of fields sampled; layout/locations ofsampled fields on the substrate; number of sites in each field;locations of the sites in the field; frequency of samples; type ofmetrology target; or measurement algorithm.

In an embodiment, one or more sampling schemes are determined based onone or more throughput models, e.g., sampling schemes that can meet thethroughput threshold. In an embodiment, one or more sampling schemes aredetermined based on the throughput model and the measurementmathematical data model. In an embodiment, a plurality of samplingschemes is determined based on the throughput model and/or themeasurement data mathematical model. For example, the number of sampledpoints is restricted by the available measurement time. If, for example,the inspection apparatus is in a lithographic apparatus or otherwisein-line with the processing of substrates in a lithocell, the totalavailable measurement time may be determined by the exposure time of afull lot. In whatever specification of available time, differentcombinations of number of substrates and number of points per substrateare possible. More points per substrate lead to a more detailed, butpotentially noisier, description of the measured data “fingerprint.”More substrates, with fewer points per substrate, lead to strongeruncertainty (e.g., noise) averaging. So, the possible combinations ofnumber of substrates sampled and/or number of points per substratesampled are determined via the inspection apparatus throughput model. Inan embodiment, the sampling scheme(s) may be determined based on aplurality of through-put models, each for a different inspectionapparatus.

In an embodiment, a sample scheme optimizer module may be used tofurther determine one or more aspects (e.g., layout of the sampledlocations/targets) for each combination of mathematical model and numberof sample points (e.g., number of substrates sampled and/or number ofpoints per substrate sampled). For example, the sample schema optimizermay take into account various constraint or limitations, such asselecting sampling locations at a minimized distance from the edge ofthe substrate to avoid non-yielding dies.

In an embodiment, the sample scheme optimizer may determine a samplingscheme for measuring data with a metrology target using a metrologyrecipe at least partially based on the through-put model of aninspection apparatus. In an embodiment, the sampling scheme may befurther based on a mathematical model. The sample scheme optimizer mayfurther determine (e.g., calculate itself or obtain from, e.g., steps935 and/or 940 described hereafter) an evaluation parameter based on themeasurement data and the sampling scheme. For example, the evaluationparameter may comprise substrate-to-substrate variation within a lot ofsubstrates, remaining uncertainty as discussed in more detailedhereafter, remaining systematic variation as described in more detailedhereafter, etc. The sample scheme optimizer may then determine if theevaluation parameter crosses a threshold. And, if the evaluationparameter is determined to cross the threshold, the sample schemeoptimizer may change the sampling scheme at least partially based on thethrough-put model (e.g., modify the sampling scheme such that thesampling scheme will still meet one or more criteria of through-putmodel). The sample scheme optimizer may further, if the sampling schemehas been changed, re-perform at least the determining the evaluationparameter based on the measurement data and the changed sampling schemeand the determining if the evaluation parameter determined based on themeasurement data and the changed sampling scheme crosses a threshold.

Fitting data using higher order basis functions typically results inincreasing sensitivity to noise. On the other hand, with increasingorder basis functions, the residuals will decrease. So, the samplescheme optimizer may account for this in arriving at sample scheme tomatch the model by balancing through a cost function that considershigher orders that reduces residuals but controls sampling to keepsensitivity to noise low. For example, the sample scheme influences thereduction of the input noise, the number of substrates that can bemeasured per lot influences the reduction of the noise, and/or the lotsampling influences the output noise. So, as part of the optimization,various different sample scheme variants can be used. For example, thenumber of substrates per lot measured may be reduced and/or the numberof sampled locations per substrate may be reduced. As a further example,more measurement points may be selected near the borders of fieldsand/or the substrate because the basis functions may “behave” the“wildest” there and so more information is desired there.

In an embodiment, the sample scheme optimizer selects an optimal subsetof measurement locations from a set of potential measurement locations.So, input to the sample scheme optimizer may be one or more mathematicalmodels that can represent the fingerprint of the measured data and ameasurement layout from which the sampling scheme may be determined(e.g., all the locations that can be measured on a substrate, e.g.,where measurement targets can be or are located). From this input, thesample scheme optimizer can evaluate the one or more models and themeasurement layout to arrive at one or more sampling schemes involving asubset of measurement locations (e.g., number and/or specific locationsof measurements) based on a cost function. The cost function may involvereducing remaining uncertainty, obtaining uniform distribution ofmeasurement locations, reducing clustering of measurement locations,reducing lot-to-lot variation, reducing substrate-to-substrate variationand/or obtaining fast execution time. In an embodiment, the user mayfurther impose a constraint, e.g., number of points to be measured,excluded certain fields or intra-field points, a parameter representingthe distribution of the points (e.g., more points toward the center ormore points toward the edge), etc. In an embodiment, the sample schemeoptimizer may impose a constraint, such as an exclusion of measurementpoints from non-yielding dies. Further, the sample scheme optimizer mayconstrain the evaluation using the through-put model, such that the oneor more sample schemes meet criteria of the through-put model. Theoutput of the sample scheme optimizer is one or more sample schemes. Inan embodiment, the sample scheme optimizer may provide a graphical userinterface to enable the inputs and constraints. Further, the graphicaluser interface may present a graphical representation of the samplescheme (e.g., a diagram or picture of a substrate with the number ofmeasurement locations graphically depicted along with their locations).The graphical user interface can also present performance informationregarding the sampling scheme such as remaining uncertainty (e.g., fordifferent directions).

Thus, the sample scheme optimizer can optimize between a sparse samplingscheme and a dense sampling scheme based on the mathematical model, theavailable layout and the through-put model. The sparse sampling may havethe lowest possible remaining uncertainty (and thus robust capture ofthe mathematical model) but may have poor coverage of the substrate andpoor robustness for mismatch between the model and the fingerprint. Onthe other hand, the dense sampling may have large or widely varyingremaining uncertainty but may have good coverage of the substrate, avoidclustering, and have good robustness for mismatch between the model andthe fingerprint.

In an embodiment, as noted above, a user may specify a constraint on thesampling scheme, for example, a maximum number of samples per substrate,a maximum number of substrates per lot sampled, etc. For example, aninterface (such as a graphical user interface) may allow the user tospecify the constraint. In an embodiment, a user may specify one or moresampling schemes to be evaluated. For example, an interface (such as agraphical user interface) may present to a user a number of samplingschemes for selection of one or more, or all, of the sampling schemesand/or allow a user to add a sampling scheme for consideration.

In an embodiment, where a new device pattern (and thus new measurementdata) is used for an otherwise same device manufacturing process andsame layer, then one or more previously determined models (butparameterized for the new measurement data) and sampling schemes may beused; thus, it may not be necessary to newly determine one or moremathematical models or newly determine one or more sampling schemes.

In an embodiment, a sample scheme optimizer selects metrology pointlocations which are most informative to the model fitting process, givena certain model. At the same time the sampling scheme optimizationalgorithm attempts to position selected metrology point locations in auniform way, such that the two objectives are balanced. In anembodiment, the sampling scheme optimization is input with a list ofpotential metrology point locations. Then, a sampling scheme isinitialized by selecting a small number of initial selected metrologypoint locations. The initial selected metrology point locations shouldbe selected according to one or more criteria in accordance with themodel. In an embodiment, each of these selected metrology pointlocations may be selected metrology point locations positioned at theedge of the effective area of a substrate, and separated equi-angularly.The initialization step may also include defining an exclusion zonearound each selected metrology point location. All metrology pointlocations which are outside the exclusion zones are candidate metrologypoint locations; i.e. “selectable” in future iterations. The exclusionzones may be circular and centered on each selected metrology pointlocation, i.e., all metrology point locations within a certain distanceof a selected metrology point location may be within an exclusion zone.Then, all candidate metrology point locations, that is all non-selectedmetrology point locations which are not within an exclusion zone, areevaluated. For each candidate metrology point location, it is calculatedhow much the informativity of the sampling scheme would improve if thatmetrology point location were selected. A criterion used in theevaluation may be D-optimality. The size of the initial exclusion zonesshould have been chosen to ensure that the initial set of candidatemetrology point locations is not too large. The number of candidatemetrology point locations should be a compromise between uniformity,informativity (e.g. D-optimality) of the final sampling scheme, andspeed of the algorithm. After evaluating all candidate metrology pointlocations, the metrology point location which, according to theevaluation, contributes the most information to the sampling scheme isthen added to the sampling scheme. It is determined whether the samplingscheme comprises sufficient selected metrology point locations. If itdoes, the sampling scheme is ready. If the sampling scheme does not havesufficient selected metrology point locations then an exclusion zone isadded around the newly selected metrology point location (the otherselected metrology point locations will also have exclusion zones).Then, it is determined whether there are a sufficient number ofcandidate metrology point locations remaining to select from, whilemaintaining the proper balance between informativity and uniformity. Inan embodiment, if it is determined that there are too few candidatemetrology point locations, this may be addressed by shrinking theexclusion zones. The exclusion zones may be shrunk for all of theselected metrology point locations comprised in the sampling scheme atthat time, or for only a subset of these selected metrology pointlocations. Then, the determination of whether there are a sufficientnumber of candidate metrology point locations remaining to select fromand (if necessary) the shrinking are repeated iteratively until thereare a sufficient number of candidate metrology point locations fromwhich to complete the sampling scheme. When there are a sufficientnumber of candidate metrology point locations, the candidate metrologypoint location evaluation and subsequent steps, are repeated. In anembodiment, the optimization may determine different sampling schemesfor different substrates. Further, different sampling schemes ofdifferent substrates may be connected such that the selected metrologypoint locations are distributed with a high degree of uniformity over aplurality of substrates: for example per lot of substrates. Inparticular, a sampling scheme optimization method may be such that ametrology point location which has been selected for a previous samplingscheme (for a previous substrate) is not selected for a subsequentsampling scheme (for a subsequent substrate) within a lot. In this wayeach selected metrology point location for the lot of substrates isunique. In an embodiment, the optimization helps ensure that, for eachindividual substrate, the normalized model uncertainty is minimized: allparameter values can be determined with improved precision. It does thisby minimizing the impact that variations in the measurements have onvariations in the model predictions.

At 935, a remaining systematic variation between the measurement data ata selected sampling scheme and a selected mathematical model for fittingthe measurement data is calculated. For example, the remainingsystematic variation may be calculated for each sampling scheme incombination with each mathematical model.

Various kinds of systematic effects during processing of the substratescan determine the systematic variation in the output of a process and isthus reflected in the measurement results as a systematic variation(e.g., systematic overlay variation), sometimes referred to as afingerprint of a process. Part (e.g., the statistically relevant part)of the fingerprint is described by the chosen mathematical model. But, aremainder is not captured by the mathematical model, but is stillsystematic. This is the remaining systematic variation. In anembodiment, the remaining systematic variation comprises a distancebetween an average of the measurement data over multiple substrates tothe selected mathematical model. In an embodiment, the remaining systemvariation may take into account a statistical (sampling) precision(e.g., a 95%-90% confidence interval) of the average. The precision isuseful to account for, for example, over-fitting, substrate-to-substratevariation and/or the number of substrates used. In an embodiment, theprecision may be, e.g., in the range of 0.1-0.8 nm, for example about0.5 nm.

The remaining systematic variation for certain substrates processed in adevice manufacturing process may be specific to particular sub-processesor devices used in the processing of the substrates. For example, theremaining systematic variation for substrates in a device manufacturingprocess may be further specified as to the one or more substrate tables,one or more etch chambers, etc. used to process the substrates, sincesubstrates may not be processed by the same substrate table, etchchamber, etc. in each iteration of the device manufacturing process andthere may be variation in the systematic effects (and thus fingerprints)caused by different substrate tables, etch chambers, etc. Further, theremaining systematic variation may be specified for lots as there may besystematic effect differences from lot to lot.

In an embodiment, the remaining systematic variation comprises remainingsystematic variation within a single substrate measured for monitoring adevice manufacturing process or substrate-to-substrate remainingsystematic variation among a plurality of substrates measured formonitoring a device manufacturing process.

At 940, a remaining uncertainty (e.g., remaining noise) of amathematical model fitting the measurement data at the selected samplingscheme and the selected mathematical model for fitting the measurementdata is calculated. For example, like the remaining systematicvariation, the remaining uncertainty may be calculated for each samplingscheme in combination with each mathematical model.

Various kinds of effects during processing of the substrates (e.g.,measurement noise, stochastic variations, etc.) can determine anuncertainty in the output of a process and is thus reflected in themeasurement results as an uncertainty (e.g., noise). Further, the mannerof taking the measurements and the mathematical modeling of themeasurements can be imprecise and varying at least in part due to noisein the measurements. So, part of the process uncertainty may bedescribed by the chosen mathematical model. But, an uncertaintyremainder is not captured by the mathematical model. This remainder isremaining uncertainty. In an embodiment, the remaining uncertaintycomprises an estimate of uncertainty of the selected fitted mathematicalmodel to the measurement data. In an embodiment, the remaininguncertainty may be determined by calculating the selected mathematicalmodel fit on sub-sampling data, per substrate (substrate pair) anddetermining the variation of the evaluation of the fit results over allsubstrates (substrate pairs) on a dense grid, e.g. the full measurementgrid. In an embodiment, the part of the remaining uncertainty thatoriginates from the within substrate uncertainty (e.g. noise) input canbe computed using the noise propagation of the mathematical model and ameasure of the within substrate uncertainty (e.g., noise) input.

In an embodiment, the remaining uncertainty may comprise a remaininguncertainty specified for within the substrate. In an embodiment, anestimate of the within-substrate remaining uncertainty can be determinedby calculating the average substrate (e.g., per substrate table),calculating for each substrate the residual with respect to thecorresponding average substrate, and then (e.g., per substrate table),take all the determined residuals as a population and calculate the 3sigma value. To check this estimate, the 3 sigma value may be comparedto a limit, optionally in different directions. For example, a goodestimate may be where the 3 sigma value is less than or equal to acertain amount, e.g., 3 sigma value less than or equal 2.5 nm in x-and/or y-direction. Another check may be whether the distribution of 3sigma values is Gaussian. Another check may be whether a plot of thestacked overlay shows little or no systematic variation/fingerprint.Another check may be whether a plot of the 3 sigma value per positionacross the substrate is substantially uniform. To improve the remaininguncertainty value (by removing systematic effects from the value), thedata may be mathematically modelled per substrate. Then the value of anaverage residual substrate is subtracted from the value of individualresidual substrates, rather than from the raw values of a substrate. Bydoing this, systematic variation can be reduced or eliminated.Similarly, within one substrate, the fields may be modeled, after whichthe value of an average residual field is subtracted from the value ofthe individual residual fields.

In an embodiment, the remaining uncertainty may comprise a modeluncertainty or normalized model uncertainty. When noise is present indata, the data may be modeled in different manners depending on thenature of the noise, the measurement (e.g., sampling) scheme used, etc.So, the model uncertainty provides a measure of noise sensitivity for amathematical model when its parameters are estimated on a givenmetrology scheme using noisy measurements. Thus, the model uncertaintycan be interpreted as a noise amplification/suppression factor fromnoise present in measurements to variations in model predicted values.The model uncertainty is a function of the mathematical model used, thelocation of measurement points, the location where the model isevaluated (interpolation extrapolation) and the number of substratesmeasured. The normalized model uncertainty (NMU) is a unitless versionof model uncertainty and doesn't change as a function of noise level.NMU<1 implicates noise suppression and NMU>1 implicates noiseamplification. Thus, the normalized model uncertainty indicates theamount of variation in modeled values scaled with the amount of noise inthe measurements. A low NMU (<1) helps ensure that a samplingscheme—mathematical model combination will lead to a consistent fit,i.e. a fit robust to noise (although it may not be a guarantee that themodel will accurately describe actual measurements). In an embodiment,the maximum NMU should be less than 0.6, less than 0.5, less than 0.4,or less than 0.3 for good noise suppression. The product of thewithin-substrate noise (e.g., the 3 sigma value) and the NMU is thewithin-substrate-noise-based output noise (e.g., remaining noise). It isa theoretical output noise and is an indicator that shows the effect ofthe chosen model and the used sample scheme. Thus, in an embodiment, thesampling scheme optimizer may optimize to reduce or minimize NMU andthen remaining uncertainty for further use in evaluation of one or moremathematical models and sampling schemes in view of the measured datamay be determined by multiplying the applicable NMU values times thewithin-substrate noise (e.g., the 3 sigma value) of the measured data.

In an embodiment, the remaining uncertainty may comprise asubstrate-to-substrate variation. This may be determined by, e.g.,calculating the average 3 sigma substrate-to-substrate variation of themathematical model across the measured data for the plurality ofsubstrates. Calculation of the output noise resulting fromwithin-substrate noise combined with substrate-to-substrate variationmay be performed by sampling each substrate with a selected number ofpoints. Then per substrate (or per combination of substrate andparticular substrate table), a selected model is fitted to the data. Theobtained model parameter values are evaluated on the completemeasurement layout. Then per position on the substrate, the standarddeviation is calculated. Then, the resulting standard deviations perposition may be averaged over all positions.

In an embodiment, the remaining uncertainty may comprise a lot to lotvariation, wherein data from multiple lots is used.

The remaining uncertainty for certain substrates processed in a devicemanufacturing process may be specific to particular sub-processes ordevices used in the processing of the substrates. For example, theremaining uncertainty for substrates in a device manufacturing processmay be further specified as to the one or more substrate tables, one ormore etch chambers, etc. used to process the substrates, sincesubstrates may not be processed by the same substrate table, etchchamber, etc. in each iteration of the device manufacturing process andthere may be variation in, e.g., noise caused by different substratetables, etch chambers, etc. Further, the remaining uncertainty may bespecified for lots as there may be uncertainty differences from lot tolot.

At 945, various plotting of the results of 930, 930 and 935 may beprovided. Such plotting may include preparing graphs, charts of data,maps of data over a substrate, etc.

At 950, an analysis of data is provided as well as a presentation ofresults and balanced advice is made. At 955, one or more mathematicalmodels for fitting measured data and one or more measurement samplingschemes for measuring data are evaluated, with respect to one or moreevaluation parameters, against measurement data across a substrate. Inan embodiment, the one or more evaluation parameters comprise aparameter representing remaining uncertainty of a mathematical modelfitting measured data. In an embodiment, the one or more evaluationparameters comprise a parameter representing remaining systematicvariation between measured data and a mathematical model fittingmeasured data. In an embodiment, the one or more evaluation parameterscomprise a first evaluation parameter and a second different evaluationparameter. In an embodiment, the first evaluation parameter comprisesthe parameter representing remaining uncertainty of a mathematical modelfitting measured data and/or the second evaluation parameter comprisesthe parameter representing remaining systematic variation betweenmeasured data and a mathematical model fitting measured data. In anembodiment, the first evaluation parameter and the second evaluation maybe combined together as a total number.

Then, one or more mathematical models and/or one or more measurementsampling schemes (of the evaluated one or more mathematical models andmeasurement sampling schemes) are identified for which the evaluationparameter crosses a threshold (e.g., exceeds a particular value, exceedsthe value of another mathematical model and/or sampling scheme, etc.).For example, the one or more mathematical models and/or one or moremeasurement sampling schemes are manually, or by automated process,selected. One or more guides, restrictions, thresholds, charts and/ortables may be provided to facilitate selection of the one or moremathematical models and/or one or more measurement sampling schemes. Forexample, a ranking may be provided of evaluated one or more mathematicalmodels and/or measurement sampling schemes. A manual or automatedcriteria may then be selection of a certain number of highest rankedmathematical models and/or measurement sampling schemes. The ranking maybe based on a single performance parameter, on a combination ofperformance parameters, or a weighted combination of performanceparameters, etc. A further manual or automated criteria may be selectionof one or more mathematical models and/or one or more measurementsampling schemes passing a certain threshold value for an evaluationparameter, optionally if those one or more mathematical models and/orone or more measurement sampling schemes do or do not pass anotherthreshold. For example, the manual or automated criteria may beevaluation of mathematical model and/or measurement sampling schemeagainst matching the fingerprint of the data (remaining systematicvariation) in relation to noise suppression (remaining uncertainty); forexample, a suitable mathematical model and/or sampling scheme may be onethat has the fingerprint capture capability of the model balancedagainst noise suppression capability. As another example, one or moremathematical models and/or one or more measurement sampling schemes maybe excluded if the remaining uncertainty is not below a certain value(e.g., excluded if NMU>0.6). As another example, one or moremathematical models and/or one or more measurement sampling schemes maybe excluded if the remaining systematic variation is above a certainvalue (e.g., excluded if the remaining systematic variation>1-5 nm,e.g., 1 nm, 1.5 nm, 2 nm, 2.5 nm, 3 nm, 3.5 nm, 4 nm, 4.5 nm or 5 nm).

In an embodiment, the results may comprise an evaluation, for eachevaluated mathematical model (e.g., a plurality of mathematical models),of an evaluation parameter against the evaluated one or more samplingschemes (e.g., a plurality of sampling schemes, such as number of pointsper substrate sampled). As an example, the results may be an evaluation,for each of a plurality of mathematical models, of a remaininguncertainty parameter value against a number of points per substratesampled (or other sampling scheme). In an embodiment, those results maybe graphed. In an embodiment, those results may be statisticallyanalyzed or otherwise evaluated against a threshold to, e.g., provideadvice to a user regarding the results. As an example, the results maybe evaluated to identify one or more combinations of mathematical modeland sampling scheme that have a maximum or minimum value (or a valuewithin 30%, within 20%, within 15%, within 10%, or within 5%) of anevaluation parameter and optionally rank those from highest to lowestrelative to the maximum or minimum value as appropriate. As a furtherexample, the results may be evaluated to identify one or morecombinations of mathematical model and sampling scheme that have acombination of good value of an evaluation parameter (e.g., high or low)in combination with a good (e.g., high) throughput value of the samplingscheme. Thus, a combination of mathematical model and sampling schemewith not the best value of an evaluation parameter may be selectedbecause it has a better throughput. An appropriate cost function (using,e.g., weighting) can be used.

In an embodiment, the evaluated one or more sampling schemes aredesigned based on, or confirmed against, a through-put model of theinspection apparatus used to measure the targets. Thus, the softwareenables determining a sampling scheme and/or a mathematical model tomonitor a process step in a lithographic process by determining thesampling scheme and the mathematical model at least partially based on athrough-put model of an inspection apparatus. So, in the case of theexample presented above regarding results of an evaluation, for each ofa plurality of mathematical models, of a remaining uncertainty parametervalue against a number of points per substrate sampled (or othersampling scheme), the software may identify or evaluate those particularspecific numbers of points per substrate (or other specific samplingschemes) that will satisfy the throughput-model of the inspectionapparatus. Thus, the user may be presented with specific combinations ofmathematical model and sampling that satisfy a through-put model andmoreover, presented with those specific combinations, or informationregarding selecting specific combinations, that obtain an optimalperformance for certain characteristics (such as good matching afingerprint of the data with good noise suppression).

In an embodiment of balanced advice, a measure of the statisticalprecision of the average substrate (i.e. used as input for determiningthe remaining systematic variation) is used with a warning limit to helpthe user identify a potential issue with the metrology target/metrologyrecipe/sampling scheme/mathematical model.

In a further embodiment of balanced advice, one or more KPIs forsubstrate-to-substrate variation across the substrate are used with awarning limit to help the user identify a potential issue with themetrology target/metrology recipe/sampling scheme/mathematical model.For example, the software may suggest to a user to implement an edgeexclusion for the sampling scheme (i.e., prevent sampling of an areanear the edge of the substrate, where the KPI used to identify thisissue may be a maximum of substrate-to-substrate standard deviationacross the substrate), to indicate a potential benefit of a substratelevel correction (where the KPI used to identify this issue may bespread of standard deviation across the substrate) or to identify apotential issue with the overall noise level of the measured data (wherethe KPI used to identify this issue may be mean of the standarddeviation across the substrate).

At 960, the user may be provided a guide on key performance indicators(KPIs). In an embodiment, a key performance indicator and/or a limit fora key performance indicator for the evaluation can be determined. Forexample, one or more KPIs may be identified and one or more thresholdsassociated with the KPIs may be determined to enable process control.For example, mean, standard deviation, variation, etc. may be identifiedas KPIs and thresholds (e.g., value not to exceed, value not to gobelow, etc.) may be determined to enable control of the process. Thesoftware may analyze various KPIs to identify one or more selected KPIsthat are statistically meaningful to the applicable mathematicalmodel/sampling scheme combination in view of, e.g., the measured data ora simulation. Similarly, the software may analyze the one or moreselected KPIs against, e.g., the measured data or a simulation, toidentify one or more statistically meaningful thresholds for the one ormore selected KPIs. For example, the software may identify mean overlayas a meaningful KPI for a particular overlay metrologytarget/recipe/model/sampling scheme combination and further identify amaximum value associated with that KPI for use during process control.So, if, for example, overlay in a device manufacturing process using theparticular overlay metrology target/recipe/model/sampling schemecombination excursions above the maximum value of the mean overlay KPI,the control of the device manufacturing process can take appropriateaction, such as reworking, determine and/or apply a change to the devicemanufacturing process (e.g., change a lithographic apparatus parameter,change an etch parameter, etc.), stop a device manufacturing process,etc.

Further, in an embodiment, at 960, the user may be able to drill downinto the measured data and into data (measured or derived data)associated with the one or more mathematical models, the one or moresampling schemes, the one or more metrology target designs, the one ormore metrology recipes and/or one or more KPIs. For example, a graphicaluser interface of the software may present a user the results asdescribed above and those results may have one or more links to view,e.g., details of the measured data (e.g., a diagram or picture of asubstrate showing the distribution of, for example, overlay results),details of the sampling scheme (e.g., a diagram or picture of asubstrate showing the locations of sampling points at fields and/or ofone or more fields showing intra-field locations), details of themathematical model (e.g., the type of model, basis functions, parametervalues, etc.), details of one or more KPIs (e.g., values for differentdirections, etc.). The drill down data may be presented on a differentscreen, as an overlapping window, etc. In an embodiment, a user mayselect a KPI for review and/or set a user-defined threshold on a KPI anddrill-down on the data (e.g., measured data, sampling scheme,mathematical model, etc.) using the KPI and/or user-defined threshold.

At 965, the one or more metrology target design—metrology recipecombinations ready for consideration for HVM may be output, optionallywith the associated performance. Further, the one or more associatedmathematical models and one or more associated sampling schemes may beoutput, optionally with the associated performance.

Once the one or more mathematical models and/or one or more samplingschemes have been determined for the selected one or more metrologytargets and associated one or more metrology recipes, it may bedesirable to verify their expected dynamic performance beforeimplementation into HVM. FIG. 10 schematically depicts a flow diagram ofan embodiment of a method of verifying expected performance.

At 1000, various preparatory data is obtained and some optionalpreparatory data processing is performed. At 1005, measurements resultsfrom one or more substrates (desirably a plurality of substrates)patterned with the one or more metrology target designs and measuredwith an inspection apparatus at their associated one or more metrologyrecipes and sampled at the associated one or more sampling schemes isobtained or received. In an embodiment, the measurement data is from aplurality of lots of substrates. For example, in an embodiment, asampling scheme may be 200 points per substrate for 6 substrates of alot and there may be data from 20 or more lots. Thus, there is obtainedmeasured across-substrate measurement data for a plurality of substratesof each lot of a plurality of lots. The data may be converted into a mapcorresponding to the layout of the substrate. In an embodiment, themeasurement data comprises one or more of: overlay data, overlay errordata, alignment data, critical dimension data, focus data and/orcritical dimension uniformity data.

At 1010, the measurement data from 1005 may optionally be processed toback-out a correction that may have been applied in the inspectionapparatus used to measure the data from 1005 and/or applied in a devicemanufacturing process used to process the substrates corresponding tothe data from 1005.

At 1015, data processing is performed including, for example,simulation. At 1020, the software may determine a correction based ondata derived from the measured data for a particular subset of lots ofthe plurality of lots. The correction may be an estimated correction. Inan embodiment, the correction comprises a change of parameter of alithographic apparatus used to expose the substrates. The correction maybe determined using the one or more mathematical models associated withthe selected one or more sampling schemes, one or more metrology targetsand one or more metrology recipes. In an embodiment, the softwareevaluates the measurement data for the plurality of substrates of theparticular lot to obtain values of parameters of the one or moremathematical models for the measurement data, wherein the data derivedfrom the measured data comprises the values of the parameters. In anembodiment, the correction may be derived using a simulation thatsimulates the device manufacturing and measuring process, e.g., animage/resist simulation model for lithography along with a substrateprocessing simulation model for development, etch, etc. and a simulationmodel for measuring a metrology target on the simulated substrate.

At 1025, the software performs a simulation, which applies thecorrection, to obtain simulated measurement data for a set of subsequentlots. In an embodiment, the simulation simulates the devicemanufacturing and measuring process, e.g., an image/resist simulationmodel for lithography along with a substrate processing simulation modelfor development, etch, etc. and a simulation model for measuring ametrology target on the simulated substrate. The simulated measurementdata for the set of subsequent lots may be compared against the measureddata for the set of subsequent lots.

At 1050, various plotting of the results of 1020 and 1025 may beprovided. Such plotting may include preparing graphs, charts of data,maps of data over a substrate, etc.

At 1030, an analysis of data is provided as well as a presentation ofresults and advice is made. At 1035, results are presented through,e.g., a user interface. The results may be, for example, a graphdepicting, for each of the measured metrologytarget/recipe/model/sampling scheme combination and the simulatedmetrology target/recipe/model/sampling scheme combination, results for aparameter (such as overlay) for each of the lots. There may be provideda graph for two different directions, e.g., X and Y directions. Thegraph(s) will give a user a representation of how well predictedperformance of the metrology target/recipe/model/sampling schemecombination from, for example, 965 matches with measured data for themetrology target/recipe/model/sampling scheme combination.

At 1040, the user may be provided a guide on key performance indicators(KPIs). In an embodiment, a key performance indicator and/or a limit fora key performance indicator for the evaluation of the simulatedmeasurement data against the measured data may be determined and/or akey performance indicator and/or a limit for a key performance indicatorfor the evaluation of the process may be determined. For example, one ormore KPIs may be identified and one or more thresholds associated withthe KPIs may be determined to enable verification between the measuredand simulated results. For example, mean, standard deviation, variation,etc. may be identified as KPIs and thresholds (e.g., value not toexceed, value not to go below, etc.) may be determined to enableverification of the metrology target/recipe/model/sampling schemecombination. For example, if the mean and/or standard deviation valuesfor the measured and simulated results are not within a certain amountof each other, the determination of a metrologytarget/recipe/model/sampling scheme combination may need to bere-performed with different parameters, different parameter values, etc.

Additionally or alternatively, for example, one or more KPIs may beidentified and one or more thresholds associated with the KPIs may bedetermined to enable process control. For example, mean, standarddeviation, variation, etc. may be identified as KPIs and thresholds(e.g., value not to exceed, value not to go below, etc.) may bedetermined to enable control of the process. The software may analyzevarious KPIs to identify one or more selected KPIs that arestatistically meaningful to the metrology target/recipe/model/samplingscheme combination in view of, e.g., the measured data or a simulation.Similarly, the software may analyze the one or more selected KPIsagainst, e.g., the measured data or a simulation, to identify one ormore statistically meaningful thresholds for the one or more selectedKPIs. For example, the software may identify mean overlay as ameaningful KPI for a particular overlay metrologytarget/recipe/model/sampling scheme combination and further identify amaximum value associated with that KPI for use during process control.So, if, for example, overlay in a device manufacturing process using theparticular overlay metrology target/recipe/model/sampling schemecombination excursions above the maximum value of the mean overlay KPI,the control of the device manufacturing process can take appropriateaction, such as reworking, determine and/or apply a change to the devicemanufacturing process (e.g., change a lithographic apparatus parameter,change an etch parameter, etc.), stop a device manufacturing process,etc.

At 1045, the user or software may select one or more metrologytarget/recipe/model/sampling scheme combinations based on KPIs and theirthresholds, e.g., those combinations with good target performance. Theone or more metrology target design—metrology recipe combinations readyfor consideration for HVM may be output, optionally with the associatedperformance. Further, the one or more associated mathematical models andone or more associated sampling schemes may be output, optionally withthe associated performance.

In an embodiment, there is provided a method comprising: evaluating,with respect to a parameter representing remaining uncertainty of amathematical model fitting measured data, one or more mathematicalmodels for fitting measured data and one or more measurement samplingschemes for measuring data, against measurement data across a substrate;and identifying one or more mathematical models and/or one or moremeasurement sampling schemes, for which the parameter crosses athreshold.

In an embodiment, the method further comprises evaluating the one ormore mathematical models and one or more measurement sampling schemeswith respect to remaining systematic variation between measured data anda mathematical model fitting measured data. In an embodiment, remainingsystematic variation comprises a distance between an average of measureddata over multiple substrates to the mathematical model. In anembodiment, the remaining systematic variation further accounts for astatistical precision of the average. In an embodiment, remaininguncertainty comprises an estimate of uncertainty of the fittedmathematical model to the measured data. In an embodiment, theidentifying comprising providing a ranking of evaluated one or moremathematical models for fitting measured data and/or evaluated one ormore measurement sampling schemes. In an embodiment, the measurementdata comprises one or more of: overlay data, overlay error data,alignment data, critical dimension data, focus data and/or criticaldimension uniformity data. In an embodiment, the method furthercomprises enabling a user to select a plurality of mathematical modelsand/or a plurality of sampling schemes for evaluation. In an embodiment,the sampling scheme comprises one or more selected from: number ofsample points per substrate, layout of sample points, and/or number ofsubstrates per lot. In an embodiment, the method further comprises:receiving measured across-substrate measurement data for a plurality ofsubstrates of each lot of a plurality of lots, where the measurementdata is modeled with the identified one or more mathematical modelsand/or measured with the identified one or more measurement samplingschemes; performing a simulation that involves applying a correction,based on data derived from the measured data for a particular subset oflots of the plurality of lots, to obtain simulated measurement data fora set of subsequent lots; and evaluating the simulated measurement datafor the set of subsequent lots against the measured data for the set ofsubsequent lots. In an embodiment, the measurement data is obtainedusing a particular measurement recipe and a particular measurementsampling scheme and the correction is determined and/or the simulationis performed using a particular mathematical model for the measurementdata. In an embodiment, the method further comprises evaluating themeasurement data for the plurality of substrates of the particular lotto obtain values of parameters of a mathematical model for themeasurement data, wherein the data derived from the measured datacomprises the values of the parameters. In an embodiment, the correctioncomprises a change of parameter of a lithographic apparatus used toexpose the substrates. In an embodiment, the method further comprisesdetermining a key performance indicator and/or a limit for a keyperformance indicator for the evaluation of the simulated measurementdata against the measured data.

In an embodiment, there is provided a method comprising: evaluating,with respect to a first evaluation parameter and a second differentevaluation parameter, one or more mathematical models for fittingmeasured data and one or more measurement sampling schemes for measuringdata, against measurement data across a substrate; and identifying oneor more mathematical models and/or one or more measurement samplingschemes, for which the first and second evaluation parameters cross athreshold.

In an embodiment, the first or second evaluation parameter comprisesremaining systematic variation between measured data and a mathematicalmodel for fitting the measured data. In an embodiment, the first orsecond evaluation parameter comprises a parameter representing remaininguncertainty of a mathematical model fitting measured data. In anembodiment, the identifying comprising providing a ranking of evaluatedone or more mathematical models for fitting measured data and/orevaluated one or more measurement sampling schemes. In an embodiment,the measurement data comprises one or more of: overlay data, overlayerror data, alignment data, critical dimension data, focus data and/orcritical dimension uniformity data. In an embodiment, the method furthercomprises enabling a user to select a plurality of mathematical modelsand/or a constraint on a sampling scheme for evaluation. In anembodiment, the sampling scheme comprises one or more selected from:number of sample points per substrate, layout of sample points, and/ornumber of substrates per lot. In an embodiment, the method furthercomprises: receiving measured across-substrate measurement data for aplurality of substrates of each lot of a plurality of lots, where themeasurement data is modeled with the identified one or more mathematicalmodels and/or measured with the identified one or more measurementsampling schemes; performing a simulation that involves applying acorrection, based on data derived from the measured data for aparticular subset of lots of the plurality of lots, to obtain simulatedmeasurement data for a set of subsequent lots; and evaluating thesimulated measurement data for the set of subsequent lots against themeasured data for the set of subsequent lots. In an embodiment, themeasurement data is obtained using a particular measurement recipe and aparticular measurement sampling scheme and the correction is determinedand/or the simulation is performed using a particular mathematical modelfor the measurement data. In an embodiment, the method further comprisesevaluating the measurement data for the plurality of substrates of theparticular lot to obtain values of parameters of a mathematical modelfor the measurement data, wherein the data derived from the measureddata comprises the values of the parameters. In an embodiment, thecorrection comprises a change of parameter of a lithographic apparatusused to expose the substrates. In an embodiment, the method furthercomprises determining a key performance indicator and/or a limit for akey performance indicator for the evaluation of the simulatedmeasurement data against the measured data.

In an embodiment, there is provided a method of determining a samplingscheme for measuring data and/or a mathematical model for fittingmeasured data, to monitor a process step in a lithographic process, themethod comprising: determining the sampling scheme and the mathematicalmodel at least partially based on a through-put model of an inspectionapparatus.

In an embodiment, the through-put model specifies a loading time of asubstrate in the inspection apparatus, an alignment time of thesubstrate in the inspection apparatus, a reposition time of thesubstrate in the inspection apparatus, a time for positioning ameasurement target within a measurement position in the inspectionapparatus and/or a time to retrieve the measurement data from ameasurement target in the inspection apparatus. In an embodiment, thedetermining comprises determining based on a plurality of through-putmodels, each for a different inspection apparatus. In an embodiment, thedetermining further comprises determining based on remaining systematicvariation between measured data and a mathematical model for fitting themeasured data. In an embodiment, the determining further comprisesdetermining based on a parameter representing remaining uncertainty of amathematical model fitting measured data. In an embodiment, theremaining systematic variation or remaining uncertainty comprisesremaining systematic variation or remaining uncertainty respectivelywithin a single substrate measured for monitoring the process step orsubstrate-to-substrate remaining systematic variation or remaininguncertainty among a plurality of substrates measured for monitoring theprocess step. In an embodiment, the inspection apparatus is aninspection apparatus in a lithographic apparatus. In an embodiment, thesampling scheme comprises one or more selected from: number of samplepoints per substrate, layout of sample points, and/or number ofsubstrates per lot.

In an embodiment, there is provided a method comprising: receivingmeasurement data of a metrology target measured according to a metrologyrecipe; determining a sampling scheme for measuring data with themetrology target using the metrology recipe at least partially based ona through-put model of an inspection apparatus; determining anevaluation parameter based on the measurement data and the samplingscheme; determining if the evaluation parameter crosses a threshold; andchanging the sampling scheme at least partially based on the through-putmodel if the evaluation parameter is determined to cross the threshold.

In an embodiment, the evaluation parameter comprisessubstrate-to-substrate variation within a lot of substrates. In anembodiment, the method further comprises determining a mathematicalmodel for fitting the measurement data and wherein the determining thesampling scheme is further based on the mathematical model. In anembodiment, the method further comprises, if the sampling scheme hasbeen changed, re-performing at least the determining the evaluationparameter based on the measurement data and the changed sampling schemeand the determining if the evaluation parameter determined based on themeasurement data and the changed sampling scheme crosses a threshold. Inan embodiment, the determining the sampling scheme comprises determiningbased on a plurality of through-put models, each for a differentinspection apparatus. In an embodiment, the method further comprisesdetermining the sampling scheme and/or a mathematical model for fittingmeasured data based on remaining systematic variation between measureddata and a mathematical model for fitting the measured data. In anembodiment, the method further comprises determining the sampling schemeand/or a mathematical model for fitting measured data based on aparameter representing remaining uncertainty of a mathematical modelfitting measured data. In an embodiment, the sampling scheme comprisesone or more selected from: number of sample points per substrate, layoutof sample points, and/or number of substrates per lot. In an embodiment,the through-put model specifies a loading time of a substrate in theinspection apparatus, an alignment time of the substrate in theinspection apparatus, a reposition time of the substrate in theinspection apparatus, a time for positioning a measurement target withina measurement position in the inspection apparatus and/or a time toretrieve the measurement data from a measurement target in theinspection apparatus. In an embodiment, the metrology target comprisesan alignment target.

FIG. 11 schematically depicts a user interface of software to providefor an embodiment of part of device manufacturing process development,monitoring and control. The embodiment of FIG. 11 is a graphical userinterface of software designed for a measurement design, setup and/ormonitoring process, such as described above. In an embodiment, theconcepts of FIG. 11 may be extended to software that enables other partsof device manufacturing process development, monitoring and control.

Referring to FIG. 11, there is depicted a plurality of graphical userinterface elements 1100. Each graphical user interface element 1100represents a step in a measurement design, setup and/or monitoringprocess and each graphical user interface element enables access by theuser to further steps in the measurement design, setup and/or monitoringprocess for the associated step of the graphical user interface element.For example, clicking on a graphical user interface element enables auser to access further steps associated with the description of thegraphical user elements. The additional steps may appear on a furtherscreen (not depicted here for clarity).

A set of one or more graphical user interface elements 1100, e.g., acolumn of one or more graphical user interface elements 1100 as shown inFIG. 11, may be associated with a particular function represented by anassociated graphical user interface element 1110. The graphical userelement 1110 itself may enable access by the user to further steps inthe measurement design, setup and/or monitoring process for theassociated function of the graphical user interface element. In anembodiment, one or more of the graphical user interface elements 1110may not enable access to further steps and may merely provideinformation regarding the particular function and the one or more stepsrepresented by the associated one or more graphical user interfaceelements 1100, e.g., the associated column of one or more graphical userinterface elements 1100 as shown in FIG. 11.

Further, there may be displayed an indicator associated with one or moreof the plurality of graphical user elements 1100, 1110. In anembodiment, the indicator indicates that a step in the measurementdesign, setup and/or monitoring process is not completed and/or that akey performance indicator associated with a step in the measurementdesign, setup and/or monitoring process has passed a threshold. In anembodiment, the indicator comprises a color of the graphical userinterface element and/or a symbol associated with the graphical userinterface element. For example, indicator 1130 (e.g., a stop sign orsimilar symbol) can indicate that a step in the measurement design,setup and/or monitoring process is not completed and/or that a keyperformance indicator associated with a step in the measurement design,setup and/or monitoring process does not successfully meet a criteria.For example, indicator 1120 (e.g., an alert sign, an exclamation sign orother similar symbol) can indicate that a key performance indicatorassociated with a step in the measurement design, setup and/ormonitoring process has passed a threshold. Additionally oralternatively, one or more of the plurality of graphical user elements1100, 1110 may be provided different colors, shading or texturedepending on particular statuses. For example, the graphical userelements 1100, 1110 with a dotted fill indicate that, e.g., the step orfunction has been completed or is otherwise OK. The dotted fillrepresents, for example, a green color, a particular shading and/or aparticular texture. Thus, the dotted fill represents, for example, thata step in the measurement design, setup and/or monitoring process iscompleted and/or that a key performance indicator associated with a stepin the measurement design, setup and/or monitoring process successfullymeets a criteria. As another example, the graphical user elements 1100,1110 with a hatched fill indicate that, e.g., the step or function hasnot been completed or is otherwise not OK. The hatched fill represents,for example, a red or orange color, a particular shading and/or aparticular texture. Thus, the hatched fill represents, for example, thata step in the measurement design, setup and/or monitoring process hasnot been completed and/or that a key performance indicator associatedwith a step in the measurement design, setup and/or monitoring processdoes not successfully meet a criteria. As another example, the graphicaluser elements 1100, 1110 with no fill indicate that, e.g., the step orfunction has not been started or cannot be accessed. The no fillrepresents, for example, a white color, a particular shading and/or aparticular texture. Thus, the no fill represents, for example, that astep in the measurement design, setup and/or monitoring process in thestep or function represented by the graphical user interface element hasnot been attempted or cannot be attempted because, e.g., one or moreearlier or dependent steps have not been completed or attempted and/or akey performance indicator associated with an earlier or dependent stepin the measurement design, setup and/or monitoring process does notsuccessfully meet a criteria.

In an embodiment, the software, despite a user engaging a particulargraphical user interface element, prevents access by the user to thefurther steps in the measurement design, setup and/or monitoring processfor the associated step of the particular graphical user interfaceelement. For example, access may be prevented to one or more of thegraphical user elements with no fill until one or more steps associatedwith, e.g., a graphical user interface element having the hatched fillor an indicator 1120 or 1130, are completed.

In an embodiment, one or more of the graphical user interface elementsor indicators may represent, or display or enable display of informationregarding, a key performance indicator and/or a guideline. For example,one or more graphical user interface elements 1100 or indicators 1120 or1130 may represent a key performance indicator and/or a guideline, suchthat the graphical user interface element enables access to a keyperformance indicator and/or guideline by, e.g., the user clicking onthe graphical user interface element. In an embodiment, one or moregraphical user interface elements 1100 or indicators 1120 or 1130 maydisplay or enable display of information regarding a key performanceindicator and/or a guideline. For example, one or more graphical userinterface elements 1100 or indicators 1120 or 1130 may display a valueof a key performance indicator or signal whether a key performanceindicator is OK or not OK. In an embodiment, the user may “fly-over” oneor more graphical user interface elements 1100 or indicators 1120 or1130 using, for example, a pointer icon, to display informationregarding a key performance indicator (e.g., a value of a keyperformance indicator or signal whether a key performance indicator isOK or not OK) and/or a guideline.

In an embodiment, one or more of the graphical user interface elementsmay have an indicator 1140 to allow updating or refreshing of data. Theuser may click or otherwise engage the indicator 1140 to cause dataassociated with one or more steps associated with the graphical userinterface to update or refresh, which may cause a change in access tosteps associated with one or more other graphical user interfaceelements and/or a change in indicator 1120 or 1130.

In an embodiment, there is provided a method comprising: displaying aplurality of graphical user interface elements, each graphical userinterface element representing a step in a measurement design, setupand/or monitoring process and each graphical user interface elementenabling access by the user to further steps in the measurement design,setup and/or monitoring process for the associated step of the graphicaluser interface element; and displaying an indicator associated with oneor more of the plurality of graphical user elements, the indicatorindicating that a step in the measurement design, setup and/ormonitoring process is not completed and/or that a key performanceindicator associated with a step in the measurement design, setup and/ormonitoring process has passed a threshold.

In an embodiment, the method further comprises, despite a user engaginga particular graphical user interface element, preventing access by theuser to the further steps in the measurement design, setup and/ormonitoring process for the associated step of the particular graphicaluser interface element. In an embodiment, the indicator comprises acolor of the graphical user interface element and/or a symbol associatedwith the graphical user interface element. In an embodiment, the methodfurther comprises displaying a graphical user interface element orindicator that represents, or displays or enables display of informationregarding, a key performance indicator and/or a guideline.

An embodiment of the invention may take the form of a computer programcontaining one or more sequences of machine-readable instructionsdescribing a method as disclosed herein, or a data storage medium (e.g.semiconductor memory, magnetic or optical disk) having such a computerprogram stored therein. Further, the machine readable instruction may beembodied in two or more computer programs. The two or more computerprograms may be stored on one or more different memories and/or datastorage media.

Any controllers described herein may each or in combination be operablewhen the one or more computer programs are read by one or more computerprocessors located within at least one component of the lithographicapparatus. The controllers may each or in combination have any suitableconfiguration for receiving, processing, and sending signals. One ormore processors are configured to communicate with the at least one ofthe controllers. For example, each controller may include one or moreprocessors for executing the computer programs that includemachine-readable instructions for the methods described above. Thecontrollers may include data storage medium for storing such computerprograms, and/or hardware to receive such medium. So the controller(s)may operate according the machine readable instructions of one or morecomputer programs. Although specific reference may be made in this textto the use of inspection apparatus in the manufacture of ICs, it shouldbe understood that the inspection apparatus described herein may haveother applications, such as the manufacture of integrated opticalsystems, guidance and detection patterns for magnetic domain memories,flat-panel displays, liquid-crystal displays (LCDs), thin film magneticheads, etc. The skilled artisan will appreciate that, in the context ofsuch alternative applications, any use of the terms “wafer” or “die”herein may be considered as synonymous with the more general terms“substrate” or “target portion”, respectively. The substrate referred toherein may be processed, before or after exposure, in for example atrack (a tool that typically applies a layer of resist to a substrateand develops the exposed resist), a metrology tool and/or an inspectiontool. Where applicable, the disclosure herein may be applied to such andother substrate processing tools. Further, the substrate may beprocessed more than once, for example in order to create a multi-layerIC, so that the term substrate used herein may also refer to a substratethat already contains multiple processed layers.

Although specific reference may have been made above to the use ofembodiments of the invention in the context of optical lithography, itwill be appreciated that the invention may be used in otherapplications, for example imprint lithography, and where the contextallows, is not limited to optical lithography. The terms “radiation” and“beam” used herein encompass all types of electromagnetic radiation,including ultraviolet (UV) radiation (e.g. having a wavelength of orabout 365, 355, 248, 193, 157 or 126 nm) and extreme ultra-violet (EUV)radiation (e.g. having a wavelength in the range of 5-20 nm), as well asparticle beams, such as ion beams or electron beams.

The term “lens”, where the context allows, may refer to any one orcombination of various types of optical components, includingrefractive, reflective, magnetic, electromagnetic and electrostaticoptical components.

References herein to crossing or passing a threshold may includesomething having a value lower than a specific value or lower than orequal to a specific value, something having a value higher than aspecific value or higher than or equal to a specific value, somethingbeing ranked higher or lower than something else (through e.g., sorting)based on, e.g., a parameter, etc.

The term “optimizing” and “optimization” as used herein refers to ormeans adjusting a lithographic apparatus, a device manufacturingprocess, etc. such that results and/or processes of lithography ordevice manufacturing have more desirable characteristics, such as higheraccuracy of projection of a design layout on a substrate, a largerprocess window, etc. Thus, the term “optimizing” and “optimization” asused herein refers to or means a process that identifies one or morevalues for one or more parameters that provide an improvement, e.g. alocal optimum, in at least one relevant metric, compared to an initialset of one or more values for those one or more parameters. “Optimum”and other related terms should be construed accordingly. In anembodiment, optimization steps can be applied iteratively to providefurther improvements in one or more metrics.

In an optimization process of a system, a figure of merit of the systemor process can be represented as a cost function. The optimizationprocess boils down to a process of finding a set of parameters (designvariables) of the system or process that optimizes (e.g., minimizes ormaximizes) the cost function. The cost function can have any suitableform depending on the goal of the optimization. For example, the costfunction can be weighted root mean square (RMS) of deviations of certaincharacteristics (evaluation points) of the system or process withrespect to the intended values (e.g., ideal values) of thesecharacteristics; the cost function can also be the maximum of thesedeviations (i.e., worst deviation). The term “evaluation points” hereinshould be interpreted broadly to include any characteristics of thesystem or process. The design variables of the system can be confined tofinite ranges and/or be interdependent due to practicalities ofimplementations of the system or process. In the case of a lithographicapparatus or device manufacturing process, the constraints are oftenassociated with physical properties and characteristics of the hardwaresuch as tunable ranges, and/or patterning device manufacturabilitydesign rules, and the evaluation points can include physical points on aresist image on a substrate, as well as non-physical characteristicssuch as dose and focus.

The invention may further be described using the following clauses:

1. A method comprising:

evaluating, with respect to a parameter representing remaininguncertainty of a mathematical model fitting measured data, one or moremathematical models for fitting measured data and one or moremeasurement sampling schemes for measuring data, against measurementdata across a substrate; and identifying one or more mathematical modelsand/or one or more measurement sampling schemes, for which the parametercrosses a threshold.

2. The method of clause 1, further comprising evaluating the one or moremathematical models and one or more measurement sampling schemes withrespect to remaining systematic variation between measured data and amathematical model fitting measured data.3. The method of clause 2, wherein remaining systematic variationcomprises a distance between an average of measured data over multiplesubstrates to the mathematical model.4. The method of clause 3, wherein the remaining systematic variationfurther accounts for a statistical precision of the average.5. The method of any of clauses 1 to 4, wherein remaining uncertaintycomprises an estimate of uncertainty of the fitted mathematical model tothe measured data.6. The method of any of clauses 1 to 5, wherein the identifyingcomprising providing a ranking of evaluated one or more mathematicalmodels for fitting measured data and/or evaluated one or moremeasurement sampling schemes.7. The method of any of clauses 1 to 6, wherein the measurement datacomprises one or more of: overlay data, overlay error data, alignmentdata, critical dimension data, focus data and/or critical dimensionuniformity data.8. The method of any of clauses 1 to 7, further comprising enabling auser to select a plurality of mathematical models and/or a plurality ofsampling schemes for evaluation.9. The method of any of clauses 1 to 8, wherein the sampling schemecomprises one or more selected from: number of sample points persubstrate, layout of sample points, and/or number of substrates per lot.10. The method of any of clauses 1 to 9, further comprising:receiving measured across-substrate measurement data for a plurality ofsubstrates of each lot of a plurality of lots, where the measurementdata is modeled with the identified one or more mathematical modelsand/or measured with the identified one or more measurement samplingschemes;performing a simulation that involves applying a correction, based ondata derived from the measured data for a particular subset of lots ofthe plurality of lots, to obtain simulated measurement data for a set ofsubsequent lots; andevaluating the simulated measurement data for the set of subsequent lotsagainst the measured data for the set of subsequent lots.11. The method of clause 10, wherein the measurement data is obtainedusing a particular measurement recipe and a particular measurementsampling scheme and the correction is determined and/or the simulationis performed using a particular mathematical model for the measurementdata.12. The method of clause 10 or clause 11, further comprising evaluatingthe measurement data for the plurality of substrates of the particularlot to obtain values of parameters of a mathematical model for themeasurement data, wherein the data derived from the measured datacomprises the values of the parameters.13. The method of any of clauses 10 to 12, wherein the correctioncomprises a change of parameter of a lithographic apparatus used toexpose the substrates.14. The method of any of clauses 10 to 13, further comprisingdetermining a key performance indicator and/or a limit for a keyperformance indicator for the evaluation of the simulated measurementdata against the measured data.15. A method comprising:

evaluating, with respect to a first evaluation parameter and a seconddifferent evaluation parameter, one or more mathematical models forfitting measured data and one or more measurement sampling schemes formeasuring data, against measurement data across a substrate; andidentifying one or more mathematical models and/or one or moremeasurement sampling schemes, for which the first and second evaluationparameters cross a threshold.

16. The method of clause 15, wherein the first or second evaluationparameter comprises remaining systematic variation between measured dataand a mathematical model for fitting the measured data.17. The method of clause 15 or clause 16, wherein the first or secondevaluation parameter comprises a parameter representing remaininguncertainty of a mathematical model fitting measured data.18. The method of any of clauses 15 to 17, wherein the identifyingcomprising providing a ranking of evaluated one or more mathematicalmodels for fitting measured data and/or evaluated one or moremeasurement sampling schemes.19. The method of any of clauses 15 to 18, wherein the measurement datacomprises one or more of: overlay data, overlay error data, alignmentdata, critical dimension data, focus data and/or critical dimensionuniformity data.20. The method of any of clauses 15 to 19, further comprising enabling auser to select a plurality of mathematical models and/or a constraint ona sampling scheme for evaluation.21. The method of any of clauses 15 to 20, wherein the sampling schemecomprises one or more selected from: number of sample points persubstrate, layout of sample points, and/or number of substrates per lot.22. The method of any of clauses 15 to 21, further comprising:receiving measured across-substrate measurement data for a plurality ofsubstrates of each lot of a plurality of lots, where the measurementdata is modeled with the identified one or more mathematical modelsand/or measured with the identified one or more measurement samplingschemes;performing a simulation that involves applying a correction, based ondata derived from the measured data for a particular subset of lots ofthe plurality of lots, to obtain simulated measurement data for a set ofsubsequent lots; andevaluating the simulated measurement data for the set of subsequent lotsagainst the measured data for the set of subsequent lots.23. The method of clause 22, wherein the measurement data is obtainedusing a particular measurement recipe and a particular measurementsampling scheme and the correction is determined and/or the simulationis performed using a particular mathematical model for the measurementdata.24. The method of clause 22 or clause 23, further comprising evaluatingthe measurement data for the plurality of substrates of the particularlot to obtain values of parameters of a mathematical model for themeasurement data, wherein the data derived from the measured datacomprises the values of the parameters.25. The method of any of clauses 22 to 24, wherein the correctioncomprises a change of parameter of a lithographic apparatus used toexpose the substrates.26. The method of any of clauses 22 to 25, further comprisingdetermining a key performance indicator and/or a limit for a keyperformance indicator for the evaluation of the simulated measurementdata against the measured data.27. A method of determining a sampling scheme for measuring data and/ora mathematical model for fitting measured data, to monitor a processstep in a lithographic process, the method comprising:

determining the sampling scheme and the mathematical model at leastpartially based on a through-put model of an inspection apparatus.

28. The method of clause 27, wherein the through-put model specifies aloading time of a substrate in the inspection apparatus, an alignmenttime of the substrate in the inspection apparatus, a reposition time ofthe substrate in the inspection apparatus, a time for positioning ameasurement target within a measurement position in the inspectionapparatus and/or a time to retrieve the measurement data from ameasurement target in the inspection apparatus.29. The method of clause 27 or clause 28, wherein the determiningcomprises determining based on a plurality of through-put models, eachfor a different inspection apparatus.30. The method of any of clauses 27 to 29, wherein the determiningfurther comprises determining based on remaining systematic variationbetween measured data and a mathematical model for fitting the measureddata.31. The method of any of clauses 27 to 30, wherein the determiningfurther comprises determining based on a parameter representingremaining uncertainty of a mathematical model fitting measured data.32. The method of clause 30 or 31, wherein the remaining systematicvariation or remaining uncertainty comprises remaining systematicvariation or remaining uncertainty respectively within a singlesubstrate measured for monitoring the process step orsubstrate-to-substrate remaining systematic variation or remaininguncertainty among a plurality of substrates measured for monitoring theprocess step.33. The method of any of clauses 27 to 32, wherein the inspectionapparatus is an inspection apparatus in a lithographic apparatus.34. The method of any of clauses 27 to 33, wherein the sampling schemecomprises one or more selected from: number of sample points persubstrate, layout of sample points, and/or number of substrates per lot.35. A method comprising:

receiving measurement data of a metrology target measured according to ametrology recipe;

determining a sampling scheme for measuring data with the metrologytarget using the metrology recipe at least partially based on athrough-put model of an inspection apparatus;determining an evaluation parameter based on the measurement data andthe sampling scheme;determining if the evaluation parameter crosses a threshold; andchanging the sampling scheme at least partially based on the through-putmodel if the evaluation parameter is determined to cross the threshold.36. The method of clause 35, wherein the evaluation parameter comprisessubstrate-to-substrate variation within a lot of substrates.37. The method of clause 35 or clause 36, further comprising determininga mathematical model for fitting the measurement data and wherein thedetermining the sampling scheme is further based on the mathematicalmodel.38. The method of any of clauses 35 to 37, further comprising, if thesampling scheme has been changed, re-performing at least the determiningthe evaluation parameter based on the measurement data and the changedsampling scheme and the determining if the evaluation parameterdetermined based on the measurement data and the changed sampling schemecrosses a threshold.39. The method of any of clauses 35 to 38, wherein the determining thesampling scheme comprises determining based on a plurality ofthrough-put models, each for a different inspection apparatus.40. The method of any of clauses 35 to 39, further comprisingdetermining the sampling scheme and/or a mathematical model for fittingmeasured data based on remaining systematic variation between measureddata and a mathematical model for fitting the measured data.41. The method of any of clauses 35 to 40, further comprisingdetermining the sampling scheme and/or a mathematical model for fittingmeasured data based on a parameter representing remaining uncertainty ofa mathematical model fitting measured data.42. The method of any of clauses 35 to 41, wherein the sampling schemecomprises one or more selected from: number of sample points persubstrate, layout of sample points, and/or number of substrates per lot.43. The method of any of clauses 35 to 42, wherein the through-put modelspecifies a loading time of a substrate in the inspection apparatus, analignment time of the substrate in the inspection apparatus, areposition time of the substrate in the inspection apparatus, a time forpositioning a measurement target within a measurement position in theinspection apparatus and/or a time to retrieve the measurement data froma measurement target in the inspection apparatus.44. The method of any of clauses 35 to 43, wherein the metrology targetcomprises an alignment target.45. A non-transitory computer program product comprisingmachine-readable instructions for causing a processor to causeperformance of the method of any of clauses 1 to 44.46. A system comprising:an inspection apparatus configured to provide a beam on a measurementtarget on a substrate and to detect radiation redirected by the targetto determine a parameter of a lithographic process; andthe non-transitory computer program product of clause 45.47. The system of clause 46, further comprising a lithographic apparatuscomprising a support structure configured to hold a patterning device tomodulate a radiation beam and a projection optical system arranged toproject the modulated onto a radiation-sensitive substrate.48. A system comprising:an alignment sensor, comprising:

an output to provide radiation from a radiation source onto a target,

a detector configured to receive radiation from the target, anda control system configured to determine alignment of two or moreobjects responsive to the received radiation; andthe non-transitory computer program product of clause 45.49. The system of clause 48, further comprising a lithographic apparatuscomprising a support structure configured to hold a patterning device tomodulate a radiation beam and a projection optical system arranged toproject the modulated onto a radiation-sensitive substrate.50. A system comprising:

a level sensor, comprising:

-   -   an output to provide radiation from a radiation source onto a        surface,    -   a detector configured to receive radiation from the surface, and    -   a control system configured to determine a position of the        surface responsive to the received radiation; and        the non-transitory computer program product of clause 45.        51. The system of clause 50, further comprising a lithographic        apparatus comprising a support structure configured to hold a        patterning device to modulate a radiation beam and a projection        optical system arranged to project the modulated onto a        radiation-sensitive substrate.        52. A method of manufacturing devices wherein a device pattern        is applied to a series of substrates using a lithographic        process, the method including inspecting at least a target        formed as part of or beside the device pattern on at least one        of the substrates using a sampling scheme as determined using        the method of any of clauses 1 to 44, and controlling the        lithographic process for the at least one substrate or another        substrate in accordance with the result of the inspecting.        53. A method of manufacturing devices wherein a device pattern        is applied to a series of substrates using a lithographic        process, the method including inspecting at least a target        formed as part of or beside the device pattern on at least one        of the substrates, wherein the inspecting is performed using a        sampling scheme as identified using the method of any of clauses        1 to 44 and/or the measured data from the inspecting is modeled        using a mathematical model as identified using the method of any        of clauses 1 to 44, and controlling the lithographic process for        the at least one substrate or another substrate in accordance        with the result of the inspecting.

While specific embodiments of the invention have been described above,it will be appreciated that the invention may be practiced otherwisethan as described. For example, the invention may take the form of acomputer program containing one or more sequences of machine-readableinstructions describing a method as disclosed above, or a data storagemedium (e.g. semiconductor memory, magnetic or optical disk) having sucha computer program stored therein.

The descriptions above are intended to be illustrative, not limiting.Thus, it will be apparent to one skilled in the art that modificationsmay be made to the invention as described without departing from thescope of the claims set out below.

1. A method comprising: evaluating, by a hardware computer system andwith respect to a parameter representing remaining uncertainty of amathematical model fitting measured data, one or more mathematicalmodels for fitting measured data and one or more measurement samplingschemes for measuring data, against measurement data across a substrate;and identifying one or more mathematical models and/or one or moremeasurement sampling schemes, for which the parameter crosses athreshold.
 2. The method of claim 1, further comprising evaluating theone or more mathematical models and one or more measurement samplingschemes with respect to remaining systematic variation between measureddata and a mathematical model fitting measured data.
 3. The method ofclaim 2, wherein remaining systematic variation comprises a distancebetween an average of measured data over multiple substrates to themathematical model.
 4. The method of claim 3, wherein the remainingsystematic variation further accounts for a statistical precision of theaverage.
 5. The method of claim 1, wherein the remaining uncertaintycomprises an estimate of uncertainty of the fitted mathematical model tothe measured data.
 6. The method of claim 1, wherein the identifyingcomprises providing a ranking of evaluated one or more mathematicalmodels for fitting measured data and/or of evaluated one or moremeasurement sampling schemes.
 7. The method of claim 1, wherein themeasurement data comprises one or more selected from: overlay data,overlay error data, alignment data, critical dimension data, focus dataand/or critical dimension uniformity data.
 8. The method of claim 1,further comprising enabling a user to select a plurality of mathematicalmodels and/or a plurality of sampling schemes for evaluation.
 9. Themethod of claim 1, wherein one or more of the one or more samplingschemes comprises one or more selected from: a number of sample pointsper substrate, a layout of sample points, and/or a number of substratesper lot.
 10. The method of claim 1, further comprising: receivingmeasured across-substrate measurement data for a plurality of substratesof each lot of a plurality of lots, where the measurement data ismodeled with the identified one or more mathematical models and/ormeasured with the identified one or more measurement sampling schemes;performing a simulation that involves applying a correction, based ondata derived from the measured data for a particular subset of lots ofthe plurality of lots, to obtain simulated measurement data for a set ofsubsequent lots; and evaluating the simulated measurement data for theset of subsequent lots against the measured data for the set ofsubsequent lots.
 11. The method of claim 10, wherein the measurementdata is obtained using a particular measurement recipe and a particularmeasurement sampling scheme and the correction is determined and/or thesimulation is performed using a particular mathematical model for themeasurement data.
 12. The method of claim 10, further comprisingevaluating the measurement data for the plurality of substrates of theparticular lot to obtain values of parameters of a mathematical modelfor the measurement data, wherein the data derived from the measureddata comprises the values of the parameters.
 13. The method of claim 10,wherein the correction comprises a change of a parameter of alithographic apparatus used to expose the substrates.
 14. The method ofclaim 10, further comprising determining a key performance indicatorand/or a limit for a key performance indicator for the evaluation of thesimulated measurement data against the measured data.
 15. Anon-transitory computer program product comprising machine-readableinstructions for causing a processor system to: evaluate, with respectto a parameter representing remaining uncertainty of a mathematicalmodel fitting measured data, one or more mathematical models for fittingmeasured data and one or more measurement sampling schemes for measuringdata, against measurement data across a substrate; and identify one ormore mathematical models and/or one or more measurement samplingschemes, for which the parameter crosses a threshold.
 16. A methodcomprising: evaluating, by a hardware computer system and with respectto a first evaluation parameter and a second different evaluationparameter, one or more mathematical models for fitting measured data andone or more measurement sampling schemes for measuring data, againstmeasurement data across a substrate; and identifying one or moremathematical models and/or one or more measurement sampling schemes, forwhich the first and second evaluation parameters cross a threshold. 17.The method of claim 16, wherein the first or second evaluation parametercomprises remaining systematic variation between measured data and amathematical model for fitting the measured data.
 18. The method ofclaim 16, wherein the first or second evaluation parameter comprises aparameter representing remaining uncertainty of a mathematical modelfitting measured data.
 19. The method of claim 16, wherein theidentifying comprises providing a ranking of evaluated one or moremathematical models for fitting measured data and/or of evaluated one ormore measurement sampling schemes.
 20. The method of claim 16, whereinthe measurement data comprises one or more selected from: overlay data,overlay error data, alignment data, critical dimension data, focus dataand/or critical dimension uniformity data.